Trajectory generation using temporal logic and tree search

ABSTRACT

Techniques for determining a trajectory for an autonomous vehicle are described herein. In general, determining a route can include utilizing a search algorithm such as Monte Carlo Tree Search (MCTS) to search for possible trajectories, while using temporal logic formulas, such as Linear Temporal Logic (LTL), to validate or reject the possible trajectories. Trajectories can be selected based on various costs and constraints optimized for performance. Determining a trajectory can include determining a current state of the autonomous vehicle, which can include determining static and dynamic symbols in an environment. A context of an environment can be populated with the symbols, features, predicates, and LTL formula. Rabin automata can be based on the LTL formula, and the automata can be used to evaluate various candidate trajectories. Nodes of the MCTS can be generated and actions can be explored based on machine learning implemented as, for example, a deep neural network.

CROSS REFERENCE TO RELATED APPLICATION

This patent application claims priority filing benefit from U.S.Provisional Patent Application No. 62/465,724, filed Mar. 1, 2017, whichis hereby incorporated by reference, in its entirety.

BACKGROUND

Various methods, apparatuses, and systems are utilized by autonomousvehicles to guide such autonomous vehicles through environmentsincluding various static and/or dynamic objects. For instance,autonomous vehicles utilize route planning methods, apparatuses, andsystems to guide autonomous vehicles through congested areas with othermoving vehicles (autonomous or otherwise), moving people, stationarybuildings, etc. In some examples, the behavior of other objects in anenvironment and road conditions can be unpredictable.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description is described with reference to the accompanyingfigures. In the figures, the left-most digit(s) of a reference numberidentifies the figure in which the reference number first appears. Theuse of the same reference numbers in different figures indicates similaror identical components or features.

FIG. 1 illustrates an example architecture for generating and executingtrajectories to control an autonomous vehicle, as described herein.

FIG. 2 illustrates a detail of an example architecture for generatingtrajectories to control an autonomous vehicle, as described herein.

FIG. 3 depicts a top level view of a scenario including an autonomousvehicle navigating a stop sign.

FIG. 4 depicts a top level view of a scenario including an autonomousvehicle navigating a three-way intersection with multiple vehicles.

FIG. 5 depicts a top level view of a scenario including an autonomousvehicle navigating a four-way intersection with multiple vehicles.

FIG. 6 illustrates a search tree for evaluating candidate trajectories,as described herein.

FIG. 7 depicts an example process for generating a trajectory for anautonomous vehicle, as described herein.

FIG. 8 depicts another example process for generating a trajectory foran autonomous vehicle, as described herein.

FIG. 9 depicts a block diagram of an example computer system forimplementing the techniques described herein.

DETAILED DESCRIPTION

This disclosure describes methods, apparatuses, and systems forgenerating trajectories for an autonomous vehicle using temporal logic(LTL) and tree search. In at least one example, the methods,apparatuses, and systems described herein are directed toheuristic-guided tree search with temporal logic constraints forgenerating trajectories for autonomous vehicles. In some examples, themethods, apparatuses, and systems described herein are directed toplanning algorithms combining learned low-level options with learnedhigh level policies over options for Task and Motion Planning (TAMP) indynamic environments, and a framework for incorporating complex taskrequirements expressed in temporal logic as applied to policy-learningfor autonomous vehicles. In some examples described in detail below,reinforcement learning with deep neural networks can be applied to taskand motion planning in complex dynamic environments. In those examples,planning problems can be expressed in terms of a set of temporal logic(e.g., Linear Temporal Logic (LTL) or Signal Temporal Logic (STL))constraints and a reward function. Additionally, or in the alternative,search algorithms, such as a Monte Carlo Tree Search (MCTS), with neuralnetwork control policies are incorporated to leverage machine learningand tree search to explore possible actions for trajectory generation.In some examples, MCTS action selection and LTL formula model checkingcan be incorporated in an autonomous driving task, where a vehicle isconfigured to drive down a road in traffic, avoid collisions, andnavigate an intersection, all while obeying the rules of the road. Theuse of such a strategy can improve computer performance requiring lessmemory, as well as having a decreased processing requirement, thusenabling such a system to be employed in real world autonomous vehiclesafety systems having to make critical safety decisions in short amountsof time with limited amounts of processing power and memory space.

TAMP approaches seek to combine high-level, “STRIPS” (e.g., StanfordResearch Institute Problem Solver)-style logical planning withcontinuous space motion planning. As can be appreciated, in the contextof autonomous vehicle controls, a problem frequently encountered is thatthe combination of the discrete and continuous portions of the statespace corresponding to speculative actions tends to explode in size forcomplex problems. The addition of temporal constraints makes searchingfor an optimal solution more difficult. In general, integrating variousmethods into a planning framework that results in reliable robot orautonomous vehicle behavior has been an open question of optimizedimplementation.

In some examples, planning can be achieved by using neural networks tolearn both low-level control policies and high-level action selectionconditions, and then using these multi-level policies as part of aheuristic search algorithm to achieve a complex task, such asdetermining a trajectory for an autonomous vehicle. In particular, taskscan be specified in an expressive temporal logical specification, andcan require reacting to a changing environment. An examplerepresentation to enable such logical specification of desired (andundesired) behaviors is Linear Temporal Logic (LTL). In examples whichemploy LTL, the continuous action parametrization, as well as theirsequencing, can be optimized to adhere to the specifications defined.

In some examples, tasks and motion planning can be formulated as aninstance of Monte Carlo Tree Search (MCTS), where each high-level optionis represented by a learned control policy trained on a set of LinearTemporal Logic (LTL) formulas. In those examples, a good tree searchpolicy can be defined, for which two complementary levels ofreinforcement learning are used. In some examples, prior informationfrom expert demonstrations can be used to initialize this search with“good” high-level discrete action distributions. In still otherexamples, such an initialization of data can be from machine learningalgorithms.

In general, determining a trajectory for an autonomous vehicle caninclude utilizing a tree search algorithm such as Monte Carlo TreeSearch (MCTS) to organize and search through possible trajectories,while using temporal logic formulas, such as Linear Temporal Logic(LTL), to verify whether the possible trajectories satisfy rules of theroad, for example, and determining various costs and constraintsassociated with possible trajectories to select a trajectory to optimizeperformance. In some instances, determining a trajectory of anautonomous vehicle can include determining a current state of thevehicle, which can include determining static symbols and dynamicsymbols which represent objects in an environment. For example, andwithout limitation, static symbols can include stop regions proximate toa stop sign, lane regions defining a lane of a road for the autonomousvehicle to traverse, static objects (e.g., buildings, obstacles, parkedvehicles, etc.) or any region of space or state of the world (e.g., suchas Washington or California), etc. Dynamic symbols can represent otherentities whose attributes change over time, examples of which includeother dynamic objects such as other vehicles, trains, pedestrians,bicyclists, etc.

Once static symbols and/or dynamic symbols are determined (e.g., from amap or a perception system), processing can include determining featuresbased on the symbols. In some instances, features can include statementsbased on symbols, whereby the statements can return a number, such as adetermination that an autonomous vehicle is 5 meters away from a stopregion.

As an initial state (e.g., a context) is populated with symbols andfeatures, additional elements referred to as predicates can beinstantiated based on the current symbols and features. For example, andwithout limitation, predicates can include logical statements based onsymbols that return values (e.g., Boolean values such as True or False,or continuous values indicating a degree of satisfaction of astatement). In one example where a symbol is an autonomous vehicle undercontrol of the current system, a predicate can evaluate as True or Falsebased on whether the autonomous vehicle is in a stop region or not(e.g., proximate to a stop sign).

As symbols, features, and predicates are added to a context indicating astate of an environment at an instant in time, processing can includedetermining temporal logic formulas, such as Linear Temporal Logic (LTL)formulas or Signal Temporal Logic (STL) formulas, that can be evaluatedbased on the present symbols, features, and/or predicates. As discussedthroughout this disclosure, temporal logic can be used to model orencode formulas about the future of paths or objects, and whetherconditions will eventually be true, whether a condition will be trueuntil another fact becomes true, etc. In some instances, the temporallogic formulas can include statements about the world that reflectproper driving behavior for an autonomous vehicle, for example. Ascandidate routes and trajectories are generated for the autonomousvehicles, the routes and trajectories can be evaluated using thetemporal logic formulas to determine if the trajectories satisfy thetemporal logic formulas, in which case, trajectories can be rejected, orevaluated with respect to other costs and constraints to select thehighest performing trajectory.

In some instances, an LTL formula can be evaluated to determine if theformula is violated or not (e.g., as a Boolean result). By way ofanother example, a temporal logic formula (such as STL) can be evaluatedto provide an indication of how well a condition is satisfied whiledetermining a cost for violating a condition (e.g., assigning a penaltyto a state as a function of how far an autonomous vehicle stops beyond astop line, in addition to or instead of assigning a Boolean value to thecondition). Additional aspects of the temporal logic formulas arediscussed throughout this disclosure.

As a context of an environment and an autonomous vehicle is determined(e.g., including the various symbols, features, predicates, temporallogic formula, etc.), some or all of the context can be used to generateone or more automaton, which can correspond to a finite state machinethat accepts trajectories as inputs to evaluate a cost of the trajectoryand/or to evaluate whether the trajectory violates any temporal logicformula associated with the one or more automaton. As used herein,references to “automata” may include one or more automaton.

Starting with an initial state (e.g., the context or automata),candidate trajectories can be evaluated using one or more tree searchalgorithms, such as a Monte Carlo Tree Search (MCTS) algorithm. Forexample, various possible trajectories can be modeled and stored as partof a MCTS search, and compared against the LTL formulas and/or evaluatedto determine costs associated with various actions. For example, as theMCTS unfolds, a snapshot (e.g., representing the context or automata)can evolve the context based on changing conditions (e.g., over time, asobjects move, based on a speculative action, etc.), and the snapshot canbe checked for compliance with the various LTL formulas. If multipletrajectories are determined not to violate the LTL formula(s), atrajectory with a lowest cost (or a highest performance, comfort, etc.)can be selected. For example, for various operations of the autonomousvehicle, or for various possible trajectories, a cost function canpenalize acceleration, jerk, lateral acceleration, yaw, steering angle,steering angle rate, etc.

In some instances, machine learning can be used to more accuratelydetermine possible trajectories to investigate using the MCTS based on acurrent state and/or learned trajectories in response to the currentstate(s) and/or tasks to be completed. For example, based on a currentstate of an environment, the MCTS, coupled with machine learning foraction exploration and selection, can determine candidate trajectoriesthat are most likely to result in satisfactory outcomes based on learnedlow-level policies (e.g., how to travel in a road lane, how to changelanes, how to stop, how not to tailgate, etc.) and learned high-levelpolicies (e.g., previously selected actions (e.g., trajectories,decisions, commands, etc.) with good outcomes). As may be understood,“good outcomes” may correspond to safe completion of tasks (e.g.,driving from point A to point B) that are efficient and comfortable.

As mentioned above, the trajectory planning operations and systemsdescribed herein can improve a functioning of a computing deviceimplemented in an autonomous vehicle by providing a robust framework bywhich planning decisions can be made in real time to optimizeperformance of the autonomous vehicle. In some instances, machinelearning algorithms can be used to determine which potentialtrajectories to evaluate based on a known current state and/or goal. Byutilizing machine learning and/or by utilizing MCTS, the operations canquickly and efficiently determine a trajectory that is safe and thatmaximizes performance based on costs and constraints. In some instances,determining static and dynamic symbols and determining a current stateusing features, predicates, LTL formulas, and automata can reduce anamount of memory and/or increase processing performance by operating onsituationally relevant data. In some instances, quickly determining atrajectory based on optimizing safety, costs, and performance cancorrespond to improved safety outcomes and/or increased comfort foroccupants of an autonomous vehicle. These and other improvements to thefunctioning of the computer are discussed herein.

The methods, apparatuses, and systems described herein can beimplemented in a number of ways. Example implementations are providedbelow with reference to the following figures. Although discussed in thecontext of an autonomous vehicle, the methods, apparatuses, and systemsdescribed herein can be applied to a variety of systems requiringautonomous or semi-autonomous control, such as industrial robots orunmanned aerial vehicles. For example, the methods, apparatuses, andsystems can be utilized in a manufacturing assembly line context, in anaerial surveying context, etc. Additionally, the techniques describedherein can be used with real data (e.g., captured using sensor(s)),simulated data (e.g., generated by a simulator), or any combination ofthe two.

FIG. 1 illustrates an example architecture 100 for generating andexecuting trajectories to control autonomous vehicles, as describedherein. For example, the architecture 100 can include computer system(s)102 including various hardware and/or software to implement aspects ofthe systems, methods, and apparatuses described herein. For example, thecomputer system(s) 102 can include a route planning module 104, adecision module 106, a trajectory module 108, a data input module 110,and a data store 112. Additionally, the architecture 100 can include avehicle control device 114 including various hardware and/or software toimplement aspects of the systems, methods, and apparatuses describedherein. In some examples, the vehicle control device 114 can be aseparate and distinct computer system, which can include an executionmodule 116, a fallback determination module 118, and a data input module120. In some examples, the computer system 102 may comprise the vehiclecontrol device 114.

In some examples, the computer system(s) 102 and vehicle control device114 can be embodied in an autonomous vehicle 122, or any other type oftransportable computer system. In other examples, the computer system(s)102 can be remotely located from the autonomous vehicle 122 and thevehicle control device 114 can be embodied in the autonomous vehicle122. In some instances, the computer system(s) 102 can provide planningfunctionality for the autonomous vehicle 122 and the vehicle controldevice 114 can provide execution functionality for the autonomousvehicle 122, as described herein.

As described above, the computer system(s) 102 can include a routeplanning module 104, a decision module 106, a trajectory module 108, adata input module 110, and a data store 112. In at least one example,individual modules of the modules (e.g., the route planning module 104,the decision module 106, and the trajectory module 108) can havedifferent frequencies of operation. As illustrated in FIG. 1, the routeplanning module 104 can have a first frequency of operation (e.g., f₁),the decision module 106 can have a second frequency of operation (e.g.,f₂), and the trajectory module 108 can have a third frequency ofoperation (e.g., f₃). In at least one example, the first frequency canbe the lowest frequency (e.g., 10 Hertz) and the third frequency can bethe highest frequency (e.g., 100 Hertz). That is, in at least oneexample, the route planning module 104 can process data at a lower speedthan the decision module 106, which can process data at a lower speedthan the trajectory module 108. The different frequencies can enable thearchitecture 100 to distribute computational resources to modules basedon a frequency in which individual modules receive updated data and/or atime period in which individual modules need to process and output data.

The route planning module 104 can be configured to determine a mostefficient route to travel from a first location (e.g., a currentlocation) to a second location (e.g., a target location). For thepurpose of this discussion, a route can be a sequence of waypoints fortravelling between two locations. As non-limiting examples, waypointsinclude streets, intersections, global positioning system (GPS)coordinates, etc. In at least one example, the route planning module 104can perform a search, such as a graph search, on top of a map toidentify a route to guide the autonomous vehicle 122 from a firstlocation to a second location. For the purpose of this discussion, a mapcan be any number of data structures modeled in two dimensions or threedimensions that are capable of providing information about anenvironment, such as, but not limited to, topologies (such asintersections), streets, mountain ranges, roads, terrain, and theenvironment in general. In at least one example, the route planningmodule 104 can utilize a graph traversal algorithm to identify a routeto guide an autonomous vehicle from a first location to a secondlocation. Graph traversal algorithms can include algorithms forunweighted graphs (e.g., breadth first search, depth first search,greedy best first, A* search, etc.) and/or weighted graphs (e.g.,Dijkstra's algorithm, weighted A* search, etc.).

In some examples, the route planning module 104 can identify two or morecandidate routes for guiding the autonomous vehicle 122 from the firstlocation to the second location. In such examples, the route planningmodule 104 can rank the two or more candidate routes based on routeplanning constraint(s). Route planning constraint(s) can include rulesof the road, travel time, travel distance, etc. In at least one example,the route planning module 104 can determine that a top-ranking candidateroute is the route for guiding the autonomous vehicle 122 from the firstlocation to the second location. The route planning module 104 canoutput a sequence of waypoints corresponding to the route to thedecision module 106.

In at least one example, the decision module 106 can receive the route(e.g., the sequence of waypoints) and can generate an instruction forguiding the autonomous vehicle 122 along at least a portion of the routefrom the first location to the second location. In at least one example,the decision module 106 can determine how to guide the autonomousvehicle 122 from a first waypoint in the sequence of waypoints to asecond waypoint in the sequence of waypoints. In some examples, theinstruction can be a trajectory, or a portion of a trajectory. In suchexamples, the decision module 106 can generate a sequence of actions(e.g., drive down the road, accelerate, change lanes, turn left, etc.)to guide the autonomous vehicle 122 along the route. In other examples,the instruction can be a policy. A policy can be used to determine atrajectory of the autonomous vehicle 122 based on real-time processedsensor data received from sensor(s) on the autonomous vehicle 122.

In at least one example, the decision module 106 can utilize one or moremodels and/or algorithms to determine an instruction for guiding theautonomous vehicle 122 from the first location to the second location inview of constraint(s). For instance, in at least one example, thedecision module 106 can utilize a combination of temporal logic (e.g.,linear temporal logic (LTL), signal temporal logic (STL), etc.) and asearch algorithm (e.g., policy tree search, Monte Carlo Tree Search(MCTS), exhaustive search, etc.) to determine one or more candidateinstructions and evaluate a performance of each of the potentialinstructions prior to determining which instruction to select.Additional details associated with the decision module 106 are describedin FIG. 2, below. The decision module 106 can output the instruction tothe trajectory module 108.

In at least one example, the decision module 106 can determine afallback instruction. The fallback instruction can be an instructionthat the autonomous vehicle 122 is to follow when an event warranting afallback action, described below, occurs. In such an example, thedecision module 106 can provide the fallback instruction to thetrajectory module 108 and/or the fallback determination module 118. Insome examples, the decision module 106 can provide a fallbackinstruction to the trajectory module 108 and/or the fallbackdetermination module 118 at the same time that the decision module 106provides an instruction to the trajectory module 108 (i.e., the decisionmodule 106 can provide two instructions to the trajectory module 108).In other examples, the decision module 106 can provide a fallbackinstruction to the trajectory module 108 and/or the fallbackdetermination module 118 at different times than when the decisionmodule 106 provides an instruction to the trajectory module 108.

In some examples, the decision module 106 can have a limited amount oftime to output an instruction. That is, in at least one example, thedecision module 106 can receive an interrupt requesting an instructionand the decision module 106 can provide an instruction responsive toreceiving the interrupt. Furthermore, processing the route to generatean instruction can be computationally expensive. Accordingly, in atleast one example, the decision module 106 can operate at a higherfrequency than the route planning module 104, as described above. In atleast one example, the decision module 106 can operate at a frequencythat is lower than the frequency required for real-time decision makingperformed by the trajectory module 108. As a non-limiting example, thedecision module 106 can operate at 10 Hertz, whereas the route planningmodule 104 can operate at one Hertz and the trajectory module 108 canoperate at 30 Hertz.

The trajectory module 108 can receive the instruction and can optimizethe instruction based on objects identified in the environment. In atleast one example, the trajectory module 108 can access, receive, and/ordetermine real-time processed sensor data to determine object(s) in theenvironment which the autonomous vehicle 122 is travelling. In the atleast one example, the trajectory module 108 can process the instructionin view of the real-time processed sensor data.

In an example where the instruction is a trajectory, the trajectorymodule 108 can leverage model(s) and/or algorithm(s), constraint(s),and/or cost(s) to optimize the trajectory. For instance, the trajectorymodule 108 can utilize model(s) and/or algorithm(s) including, but notlimited to, differential dynamic programming, interior pointoptimization, sequential quadratic programming, etc. to refine thetrajectory. In at least one example, the constraint(s) can include, butare not limited to, cost(s), comfort, safety, rules of the road, etc. Inat least one example, the cost(s) can include, but are not limited to,performance (e.g., speed), minimizing lateral acceleration, positioningin a lane, etc. In at least one example, the model(s) and/oralgorithm(s) can include bi-directionality. In such an example, avelocity of the autonomous vehicle 122 can be optimized to include apositive, a negative, or a zero value. In at least one example, arotation of the autonomous vehicle 122 can be described using Euclidianmatrices. As a result, a same model and/or algorithm can be used foroptimizing a trajectory having different types of waypoints (e.g., road,intersection, roundabout, etc.). Based at least in part on processingthe trajectory, in view of the real-time processed sensor data, thetrajectory module 108 can generate an output trajectory.

In an example where the instruction is a policy, the trajectory module108 can leverage model(s) and/or algorithm(s), constraint(s), and/orcost(s) to generate a trajectory based on the policy and real-timeprocessed sensor data. For instance, the trajectory module 108 canutilize model(s) and/or algorithm(s) including, but not limited to,differential dynamic programming, interior point optimization,sequential quadratic programming, etc. to generate a trajectory based onthe policy. For the purpose of this discussion, the trajectory can becalled an output trajectory.

As described above, the trajectory module 108 can access, receive,and/or determine real-time processed sensor data. The trajectory module108 can leverage the real-time processed sensor data to generate anoutput trajectory. The trajectory module 108 can utilize a more detailedmodel of the autonomous vehicle 122 than the decision module 106.Processing that utilizes such a detailed model can be computationallyexpensive. Additionally, the trajectory module 108 can output an outputtrajectory within a predetermined amount of time after receiving thereal-time processed sensor data. For instance, in at least one example,the trajectory module 108 can receive an interrupt requesting an outputtrajectory and the trajectory module 108 can provide an outputtrajectory responsive to receiving the interrupt. In some examples, thetrajectory module 108 can have less time to output an output trajectorythan the decision module 106 has to output a trajectory, in order toaccount for obstacles (e.g., another vehicle, pedestrian, etc.) orconditions. Accordingly, the trajectory module 108 can operate at ahigher frequency than the route planning module 104 and/or the decisionmodule 106, as described above.

In at least one example, the trajectory module 108 can receive afallback instruction from the decision module 106. In such examples, thetrajectory module 108 can generate an output fallback trajectory basedon processing the fallback instruction in a substantially similar manneras described above. In some examples, as described above, the trajectorymodule 108 can output the output trajectory and the output fallbackinstruction at the same time.

The data input module 110 can receive input from one or more sensors onthe autonomous vehicle 122. In at least one example, the autonomousvehicle 122 can have one or more sensors which can include lightdetection and ranging (LIDAR) sensors for capturing LIDAR data forsegmentation and/or classification, camera sensors for capturing visiondata for image segmentation and/or classification, radio detection andranging (RADAR) sensors for capturing range, angle, and/or velocity ofobjects in an environment, sound navigation and ranging (SONAR) sensorsfor capturing acoustic information of objects in an environment, etc. Inat least one example, the data input module 110 can receive data fromeach of the sensors (e.g., LIDAR sensors, camera sensors, RADAR sensors,SONAR sensors, etc.) described above and can process the data toidentify objects and determine information about the objects in theenvironment. Additionally, the autonomous vehicle 122 can includeultrasonic transducers, wheel encoders, microphones, inertialmeasurement unit(s) (IMU), accelerometers, gyroscopes, magnetometers,temperature sensors, humidity sensors, light sensors, global positioningsystem (GPS) sensors, etc. The data input module 110 can process datareceived from the one or more sensors to determine a state of theautonomous vehicle 122 at a particular time. That is, the data inputmodule 110 can process data received from the one or more sensors todetermine a position of the autonomous vehicle 122 at a particular time,an orientation of the autonomous vehicle 122 at a particular time, avelocity of the autonomous vehicle 122 at a particular time, etc. In atleast one example, the one or more sensors and the data input module 110may be associated with a perception system for performing data analysissuch as segmentation and classification. As described below, such data(e.g., real-time processed sensor data) can be used by the trajectorymodule 108 for generating output trajectories. Additionally, such data(e.g., real-time processed sensor data) can be used by the routeplanning module 104 for planning routes and/or the decision module 106for generating instructions.

The data store 112 can store data so that it can be organized, updated,and accessed. In at least one example, the data store 112 can includemodel(s) 124, constraint(s) 126, policy(s) 128, logical rule(s) 130,system identification data 132, predictive data 134, map(s) 136, etc.The model(s) 124 can include model(s) of the autonomous vehicle 122,model(s) of other objects in the environment, decision model(s), etc.

Any number of vehicle models can be used with the systems and methodsdiscussed herein. In some examples, a vehicle model having coarsediscretizations of possible actions and/or predicted steering angle canbe used. The choice of a particular vehicle model can be made togenerate feasible trajectories that could be executed by an autonomousvehicle.

In one example, the state of each road world entity, i, can be definedby w_(i)=[p_(x), p_(y), θ, ν, ψ], where (p_(x),p_(y)) are the vehicle'sinertial coordinates, θ its bearing, and ν its linear velocity. Further,a road world control input can comprise one or more of an acceleration aand a steering angle rate {dot over (ψ)}, such that u=[u₁, u₂]:=(a, {dotover (ψ)}), though any number of other control inputs are contemplated.

Continuing in such an example, dynamics of the planning agent (e.g., theautonomous vehicle) can be modeled as:

$\begin{matrix}{{\overset{.}{p}}_{x} = {v\;\cos\;\theta}} & (1) \\{{\overset{.}{p}}_{y} = {v\;\sin\;\theta}} & (2) \\{\overset{.}{\theta} = {\frac{v}{L}\tan\;\psi}} & (3) \\{\overset{.}{v} = u_{1}} & (4) \\{\overset{.}{\psi} = u_{2}} & (5)\end{matrix}$where L is the vehicle wheelbase length. In some examples, a fixed timestep of 0.1 seconds can be used for learning and for all experiments,though any other time step is contemplated. As can be understood, insome examples, dynamics of the autonomous vehicles can be stored as oneof the model(s) 124.

The constraint(s) 126 can include cost(s), comfort, safety, rules of theroad, etc. The policy(s) 128 can include manual policies, learnedpolicies, control policies, option policies, etc. Example policiesinclude, but are not limited to, a minimum distance to maintain fromother vehicles, maximum acceleration rates, driving rules (e.g., staywithin a lane, don't cross double yellow lines, etc.), and the like. Thelogical rule(s) 130 can include reasoned rules of the road, etc. Thesystem identification data 132 can include information about theautonomous vehicle 122 over time. The predictive data 134 can includeone or more snapshots of the autonomous vehicle 122 at future time(s),and/or can include predictions of behavior of other dynamic objects(e.g., other vehicles) proximate to the autonomous vehicle 122 at futuretime(s). The map(s) 136 can include data structures modeled in twodimensions or three dimensions that are capable of providing informationabout an environment, such as, but not limited to, topologies (such asintersections), streets, mountain ranges, roads, terrain, and theenvironment in general.

As described above, the vehicle control device 114 can be a separate anddistinct computer system, which can include an execution module 116, afallback determination module 118, and a data input module 120. In someexamples, the vehicle control device 114 can access the data inputmodule 110 and/or data store 112 associated with the computer system(s)102.

The execution module 116 can receive the output trajectory from thetrajectory module 108 and can compute commands for actuating steeringand acceleration of the autonomous vehicle 122 to enable the autonomousvehicle 122 to follow the output trajectory. In at least one example,the execution module 116 can receive the output trajectory and cancompute a steering angle and velocity to enable the autonomous vehicle122 to follow the output trajectory. A non-limiting example of analgorithm that the execution module 116 can use is provided below.δ=−P*ela  (6)ela=e+xla*sin(ΔΨ)  (7)In equations (6) and (7) above, a gain (e.g., a predetermined constantvalue) is represented by P, lateral error is represented by e, lookaheaderror is represented by ela, heading error is represented by ΔΨ,lookahead distance (parameter) is represented by xla, and steering angleis represented by δ.

The fallback determination module 118 can access, receive, and/orgenerate fallback trajectory(s). As described above, a fallbacktrajectory can be a trajectory that the autonomous vehicle 122 is tofollow responsive to determining an occurrence of an event warranting afallback action. In at least one example, an event can be a problem withthe computer system(s) 102. For instance, a sensor associated with thecomputer system(s) 102 can fail or a component of the autonomous vehicle122 can malfunction (e.g., tire pops, windshield shatters, etc.). Or, anevent can be associated with a lack of communication from the computersystem(s) 102 and/or of responsiveness of the computer system(s) 102. Insome examples, an event can be an object that is within a thresholddistance of the autonomous vehicle 122, an object that is predicted tobe within a threshold distance of the autonomous vehicle 122, or aprobability of an accident (i.e., collision) exceeding a thresholdprobability. Moreover, in at least one example, an event can beassociated with an occupancy status of the autonomous vehicle 122. Anoccupancy status of the autonomous vehicle 122 can indicate when apassenger in the autonomous vehicle 122 becomes incapacitated, when apassenger (or object associated with a passenger) is defenestrated fromthe autonomous vehicle 122, etc. Furthermore, an event can be associatedwith a status of a drivable surface associated with the autonomousvehicle 122. The status of the drivable surface can indicate when adrivable surface is impassible (e.g., a bridge has collapsed, weatherhas caused an impassible condition, etc.). In yet additional and/oralternative examples, an event can be associated with a level ofconfusion associated with the computer system(s) 102 exceeding aconfusion threshold. For instance, the computer system(s) 102 canreceive real-time processed sensor data and may not be able to identifyone or more objects in the environment surrounding the autonomousvehicle 122, which can indicate a level of confusion.

In at least one example, a fallback trajectory can correspond to afallback action, which may correspond to a safety maneuver, such asaggressively stopping the autonomous vehicle 122, driving to theshoulder of the road and stopping, etc. In some examples, the fallbackaction may not be “smooth” to a passenger, but may safely navigate asituation responsive to an occurrence of an event. In some examples, thefallback determination module 118 can receive an output fallbacktrajectory from the decision module 106 and/or the trajectory module108. In such examples, the fallback determination module 118 can storethe output fallback trajectory for a predetermined period of time, untila new output fallback trajectory is received, etc. In other examples,the fallback determination module 118 can generate a fallback trajectorybased at least in part on real-time processed sensor data and/orhard-coded rule(s). In at least one example, a fallback trajectory canbe determined based on a type of event. That is, different events canwarrant different fallback actions.

In at least one example, the fallback determination module 118 candetermine that the autonomous vehicle 122 is about to collide with anobstacle. That is, the fallback determination module 118 can leveragereal-time processed sensor data to determine that an object is within athreshold distance of the autonomous vehicle 122. Based at least in parton determining that the autonomous vehicle 122 is about to collide withthe obstacle, the fallback determination module 118 can access and/orgenerate a fallback trajectory which causes the autonomous vehicle 122to perform a fallback action. Additionally and/or alternatively, in atleast one example, the fallback determination module 118 can determinethat the vehicle control device 114 is not receiving outputtrajectory(s) and/or other communications from the computer system(s)102. That is, the fallback determination module 118 can determine thatthe computer system(s) 102 are nonresponsive and/or noncommunicative.Based at least in part on determining that the computer system(s) 102are nonresponsive and/or noncommunicative, the fallback determinationmodule 118 can access and/or generate the fallback trajectory responsiveto such a determination.

In at least one example, the fallback determination module 118 canprovide a fallback trajectory to the execution module 116 and theexecution module 116 can compute commands for actuating steering andacceleration of the autonomous vehicle 122 to enable the autonomousvehicle 122 to follow the fallback trajectory.

The data input module 120 can receive input from one or more sensors onthe autonomous vehicle 122. In at least one example, the autonomousvehicle 122 can have one or more sensors which can include LIDAR sensorsfor capturing LIDAR data for segmentation and/or classification, camerasensors for capturing vision data for image segmentation and/orclassification, RADAR sensors for capturing range, angle, and/orvelocity of objects in an environment, SONAR sensors for capturingacoustic information of objects in an environment, etc. In at least oneexample, the data input module 120 can receive data from each of thesensors (e.g., LIDAR sensors, camera sensors, Radar sensors, sonarsensors, etc.) described above and can process the data to identifyobjects and determine information about the objects in the environment.Additionally, the autonomous vehicle 122 can include ultrasonictransducers, wheel encoders, microphones, inertial measurement unit(s)(IMU), accelerometers, gyroscopes, magnetometers, temperature sensors,humidity sensors, light sensors, GPS sensors, etc. The data input module120 can process data received from the one or more sensors to determinea state of the autonomous vehicle 122 at a particular time. That is, thedata input module 120 can process data received from the one or moresensors to determine a position of the autonomous vehicle 122 at aparticular time, an orientation of the autonomous vehicle 122 at aparticular time, a velocity of the autonomous vehicle 122 at aparticular time, etc.

Such data (e.g., real-time processed sensor data) can be used by thefallback determination module 118 to determine when a fallback action iswarranted and/or to generate a fallback trajectory. Additionally and/oralternatively, such data (e.g., real-time processed sensor data) can beused by the execution module 116 for computing a steering angle andvelocity to enable the autonomous vehicle 122 to follow the outputtrajectory and/or fallback trajectory.

In at least one example, the execution module 116 and the fallbackdetermination module 118 can have a fourth frequency of operation (e.g.,f₄) that is different than the route planning module 104, the decisionmodule 106, and/or the trajectory module 108. In at least one example,the execution module 116 and the fallback determination module 118 canoperate at a highest frequency to enable the execution module 116 andthe fallback determination module 118 to make near real-time decisions.

Additional details of the computer system(s) 102 and/or the vehiclecontrol device 114 are provided below in connection with FIG. 9.

As described above, in at least one example, individual of the modulescan have different frequencies of operation. For instance, the routeplanning module 104 can have a first frequency of operation (e.g., f₁),the decision module 106 can have a second frequency of operation (e.g.,f₂), the trajectory module 108 can have a third frequency of operation(e.g., f₃), and the execution module 116 and the fallback determinationmodule 118 can have a fourth frequency of operation (e.g., f₄). In atleast one example, the first frequency can be the lowest frequency(e.g., 10 Hertz) and the fourth frequency can be the highest frequency(e.g., 100 Hertz), as described above. This configuration enables thearchitecture 100 to distribute computational resources to modules basedon a frequency in which individual modules receive updated data and/or atime period in which individual modules need to process and output data.

Additionally, as described above, the computer system(s) 102 can beseparate and distinct from the vehicle control device 114. In someexamples, this configuration can enhance safety, redundancy, andoptimization. As described above, in at least one example, the fallbackdetermination module 118 can determine the occurrence of an eventwarranting a fallback action, as described above. In such an example,the fallback determination module 118 can access and/or generate afallback trajectory, which can be executed by the execution module 116.In at least one example, the fallback instruction can correspond toinstructions for aggressively (but safely) stopping the autonomousvehicle 122. In other examples, the fallback instruction can correspondto performing some other safety maneuver.

Furthermore, as described above, the data input module 120 can receivesensor data from one or more sensors. The data input module 120 canprocess sensor data received from the one or more sensors to determinethe state of the autonomous vehicle 122 locally. The execution module116 can utilize the state of the autonomous vehicle 122 for computing asteering angle and velocity to enable the autonomous vehicle 122 tofollow the output trajectory without having to communicate with thecomputer system(s) 102. That is, separating the vehicle control device114, which is executing the execution module 116, from the computersystem(s) 102, which are executing one or more other modules (e.g.,route planning module 104, decision module 106, trajectory module 108,etc.), can conserve computational resources expended by the vehiclecontrol device 114 by enabling the vehicle control device 114 to executetrajectory(s) locally.

In an additional and/or alternative example, the separation of thecomputer system(s) 102 from the vehicle control device 114 can be usefulfor troubleshooting. For instance, a programmer can identify an error,flaw, failure, fault, etc. associated with either the computer system(s)102 or the vehicle control device 114. Accordingly, the programmer cantroubleshoot either the computer system(s) 102 or the vehicle controldevice 114, instead of troubleshooting the entire system.

Furthermore, the separation of the computer system(s) 102 from thevehicle control device 114 can enable easier safety certification of thevehicle control device 114. That is, by separating the planningfunctionality (on the computer system(s) 102) from the executionfunctionality (on the vehicle control device 114), the architecture 100can minimize the amount of code executing on the vehicle control device114, making safety certification(s) easier to obtain.

FIG. 2 illustrates a detail of an example architecture 200 forgenerating trajectories to control an autonomous vehicle, as describedherein. The example architecture 200 illustrates aspects of the decisionmodule 106 receiving inputs from the data input module 110 and the datastore 112 to generate one or more routes or trajectories to be used incontrolling the autonomous vehicle.

In general, the decision module 106 can include a static symbol scanningmodule 202 and a dynamic symbol scanning module 204 to receive and/orgenerate information about an environment of the world. For example, thestatic symbol scanning module 202 can receive map information from themap(s) 136, whereby static objects can be encoded or annotated into themap(s) 136. As can be understood, the static symbol scanning module 202can scan the map(s) 136 to determine any static symbols within athreshold distance (e.g., a horizon) of the autonomous vehicle. Forexample, a threshold distance or horizon can be within 100 meters of theautonomous vehicle, although any distance can be used. In someinstances, the horizon can be constrained or limited to area in apotential area of travel of the autonomous vehicle (e.g., in thevehicle's path) although it can be appreciated that any horizon can beused. Examples of static symbols include stop regions (e.g., areasproximate to a stop sign), lane regions (e.g., areas corresponding to alane on a road), intersection regions (e.g., intersections controlled bytraffic light(s), intersections controlled by stop/yield signs,uncontrolled intersections, etc.), turn regions (e.g., areas ofintersections for turning), post turn regions (e.g., areas of a roadfollowing a turn), buildings, obstacles, trees, signs, etc. Examples ofdynamic symbols include other vehicles, pedestrians, etc.

The static symbol scanning module 202 can receive information associatedwith static symbols from the map(s) 136, as discussed above, or from theperception system. For example, the data input module 110 can providedata from any number of sensors, including LIDAR sensors, camerasensors, RADAR sensors, SONAR sensors, etc., and can performsegmentation and/or classification on captured data to identify anystatic and/or dynamic objects, and can provide information associatedwith the static and/or dynamic objects (e.g., a bounding box and/orlabel) to one or both of the static symbol scanning module 202 and thedynamic symbol scanning module 204. In some instances, the dynamicsymbol scanning module 204 can receive information associated withdynamic objects from the predictive data 134, such as a predictedbehavior of a particular object. In some instances, the predictive data134 can include one or more possible trajectories associated withdynamic objects, such as potential paths for other vehicles on the road.The predictive data 134 can be based in part on previously observedbehavior that is used to predict future behavior of the various dynamicobjects.

Further, the dynamic symbol scanning module 204 can receive one or moreof the policies 128 associated with one or more dynamic objects. Forexample, a policy of the policy(s) 128 can include information aboutcapabilities and/or behavior of the dynamic symbols in an environment(e.g., with respect to pedestrians, they can walk across the road at acrosswalk, walk along a sidewalk etc.).

As the static symbol scanning module 202 and the dynamic symbol scanningmodule 204 receive symbol data corresponding to an environment, thesymbol data can be used to build a context of the environment in thecontext module 206. For example, the symbol data can be stored as one ormore symbol(s) 208. As symbols are input to the context module 206, thedecision module 106 can include functionality to determine variousfeature(s) 210, predicate(s) 212, temporal logic (TL) formula 214, andautomata 216. As discussed herein, the feature(s) 210 can includestatements based on symbols that return a number, such as adetermination that an autonomous vehicle is 5 meters away from a stopregion.

Further, the predicates 212 can include logical statements based onfeatures and/or symbols that return values (e.g., Boolean values such asTrue or False, or continuous values indicating a degree of satisfactionof a statement). In one example where a symbol is an autonomous vehicleunder control of the current system, a predicate can be evaluated asTrue or False based on whether the autonomous vehicle is in a stopregion or not (e.g., proximate to a stop sign). In some examples,features 210 can be generated for a subset of static and/or dynamicobjects present in a horizon. In an example where the autonomous vehicleis driving in traffic including other vehicles, features 210 can becomputed for vehicles ahead of and behind the autonomous vehicle in thesame lane, as well as in the neighboring lane, and for the nearestvehicles to the left and right on the cross street. As can beunderstood, limiting a number of features can improve a functioning ofthe decision module 106 by reducing an amount of data and/orpossibilities to consider for planning purposes.

The TL formulas 214 can be evaluated based on the present symbols,features, and/or predicates. As discussed throughout this disclosure,temporal logic (TL) can be used to model or encode formulas about thefuture of paths or objects, and whether conditions will eventually betrue, whether a condition will be true until another fact becomes true,etc. In some instances, the temporal logic may include signal temporallogic (STL), interval temporal logic (ITL), computational tree logic(CTL), property specification language (PSL), Hennessy-Milner logic(HML), etc. In some instances, in addition to or instead of TL, thesystems described herein can use planning domain definition language(PDDL) and/or STRIPS (Stanford Research Institute Problem Solver). Insome instances, references to a particular implementation of temporallogic is not intended to limit the example to the particularimplementation. In some instances, the TL formulas 214 can includestatements about the world that reflect proper driving behavior (e.g.,rules of the road, right-of-way rules, rules against tailgating, etc.)for an autonomous vehicle, for example. As candidate routes andtrajectories are generated for the autonomous vehicles, the routes andtrajectories can be evaluated using the TL formulas 214 to determine ifthe trajectories satisfy the TL formulas 214, in which case,trajectories can be rejected, or evaluated with respect to other costsand constraints to select the highest performing trajectory. In someinstances, the temporal logic formulas can be used to automaticallygenerate a state machine that can be used by components of the computersystems 102 and/or the vehicle control device 114 for tasks in additionto generating and/or rejecting candidate trajectories.

In some instances, a TL formula 214 can be evaluated (e.g., by aprocessor associated with the decision module 106) to determine if aformula is violated or not (e.g., as a Boolean result). By way ofanother example, a TL formula 214 can be evaluated (e.g., utilizing STL)to provide an indication of an extent to which a condition is satisfied,while determining a cost for violating a condition (e.g., assigning apenalty to a state as a function of how far an autonomous vehicle stopsbeyond a stop line, rather than or in addition to assigning a Booleanvalue to the condition). Additional aspects of the TL formula 214 arediscussed throughout this disclosure.

As a context of an environment and an autonomous vehicle are determinedby the decision module 106 (e.g., including the various symbols,features, predicates, TL formula, etc.), the context can be used togenerate the automata 216, which can correspond to a finite statemachine that accepts trajectories as inputs to evaluate a cost of thetrajectory and/or whether the trajectory violates any TL formula. Insome instances, the automata 216 can include Rabin automata.

As can be understood, the context module 206 can include situationallyrelevant information, and therefore the information populated into thecontext module 206 can be based on the present symbols 208, and can beselected from one or more predefined libraries.

For example, the decision module 106 can include a feature librarymodule 218, a predicate library module 220, and a temporal logic (TL)library module 222. As various symbols are introduced into the contextmodule 206, the feature library module 218 can determine one or morefeatures that are situationally relevant based on present symbols and/orother features, and can populate the features 210 of the context module206. Similarly, as various symbols and features are introduced into thecontext module 206, the predicate library module 220 can determine oneor more predicates that are situationally relevant based on presentsymbols, features, and or other predicates, and can populate thepredicates 212 of the context module 206. As various symbols, features,and predicates are introduced into the context module 206, the TLformula library module 222 can determine one or more TL formulas thatare situationally relevant based on present symbols, features, and/orpredicates, and can populate the TL formula 214 of the context module206. Additional examples of various symbols, features, predicates, andTL formula are discussed in FIGS. 3, 4, and 5, as well as throughout thedisclosure.

As the context module 206 is populated with the various symbols 208,features 210, predicates 212, and TL formula 214, the TL formula 214 canbe converted to the automata 216, which can operate as a finite statemachine to accept trajectories as inputs for model checking, asdiscussed herein. Examples of various automata can include, but are notlimited to Rabin automata, Streett automata, Büchi automata, Mullerautomata, etc. In some instances, the automata can accept any number offinite inputs or infinite inputs. In some instances, the automata caninclude any number of finite states, or can include an infinite numberof states. In some instances, the automata can include deterministic,non-deterministic, or alternation automata. In some instances, theautomata can include nondeterministic or deterministic finite statemachines, deterministic pushdown automata, linear bounded automata,Turing machines, non-deterministic or deterministic Büchi automata,Rabin automata, Streett automata, Parity automata, Muller automata, etc.

Further, the decision module 106 can include a tree search module 224and a trajectory generation module 226 for generating and testingpossible trajectories to control the autonomous vehicle. In someinstances, the tree search module 224 can generate a tree includingvarious nodes, where each node of the tree can represent a speculativecontext corresponding to a different potential trajectory. In someinstances, the tree search module 224 may utilize a Monte Carlo TreeSearch. As the tree search module 224 and the trajectory generationmodule 226 build the tree, the modules simultaneously evolve a contextof the environment corresponding to different trajectories, and cancompare each evolved context (e.g., which can be referred to as asnapshot) against each TL formula or automata to determine whether thetrajectory violates a TL formula, and if so, and in some examples, canprovide an indication of a cost associated with such a violation. Thetree search module 224 can include machine learning that learns andguides the processing to select actions (e.g., trajectories) that aremost likely to be correct, based on a current context, to test varioustrajectories.

In general, and in some examples, the decision module 106 can be modeledunder consideration as a Markov Decision Process (MDP). In such anexample, learning can be performed over a sequence of time steps (see,e.g., FIG. 6). For example, at step t, the autonomous vehicle (e.g., thedecision module 106) can observe a state, s_(t)∈S, which represents thesensed state of the system, which is to say, an internal state as wellas what the decision module 106 perceives about an environment itoperates in. In some examples, S can be defined to include dynamic andkinematic models of the autonomous vehicle and the environment. Based ons, the autonomous vehicle can select an action a_(t)∈A from an availableset of actions, A. On performing a_(t) on the autonomous vehicle havinga state s_(t), the autonomous vehicle can receive an immediate reward,r_(t)∈R, and move to a state s_(t+1). Such actions and rewards can beassociated with a particular goal of the autonomous vehicle. Forexample, the goal of the autonomous vehicle can be to maximize itscumulative reward. Additionally, or in the alternative, such a goal canbe based, at least in part, on a time-discounted sum of rewards over atime horizon (which can be finite or infinite). In general, a mappingfrom states to actions for a particular autonomous vehicle can bedefined as a policy, π:S→A.

In some instances, the decision module 106 can be modeled as asemi-Markov Decision Process (sMDP), such that the decision module 106can utilize information for multiple previous time steps. In general,the decision module 106 can utilized a policy over “actions” or“options”, which maps from a state space associated with the decisionmodule 106 to a high-level action. Examples include a policy to staywithin a lane, a policy to change lanes, etc. This option (or action)can also be represented as a second policy, which maps from state tocontrols (e.g., steering angle rate, acceleration, etc.). As discussedherein, a tree search algorithm (e.g., MCTS) can select actions to beperformed from particular states and executes such as selected actionsfor some length of time. When the policy is executed, the plannerrepeatedly calls the action policy to get an acceleration and steeringangle rate pair, then receives input regarding the environment todetermine what effect the acceleration and/or steering angle rate inputshad, and then evaluates again.

Additionally, or in the alternative, a Q-function (a feature of a MarkovDecision Process (MDP)) can be used to provide additional insight intothe model. The value of Q^(π)(s,a) is defined to be the best cumulativereward that can be obtained in the future under policy π afterperforming action a, given a current state, s. The Q-function is thus alocal measure of the quality of action a. Similarly, the “valuefunction” of an MDP V^(π):S→? is a local measure of the quality of sunder policy π. In some examples, for an optimal policy π*, V* and Q*can be obtained as fixed points using Bellman's equation. In someexamples, either the V function or the Q function can be approximated.

In some examples, a policy can be learned iteratively. In a non-limitingexample, an actor-critic policy iteration method can be used. In such anexample, during each iteration, i, the “critic” estimates Q^(π) ^(i) ,and the “actor” uses this to improve π_(i) to determine π_(i+1).

In some examples, the MDP can be solved by picking from a hypothesisclass of policies π composed using a set of high-level options, whichare themselves learned from a hypothesis class of parametrized controlpolicies using a deep neural network. In such an example, the optimalpolicy cannot be contained in this hypothesis class, but a goodapproximation can be obtained.

Additional details of the TL library module 222, and temporal logic ingeneral, are discussed below. In one or more examples, properties ofplans can be defined in terms of a set of atomic statements (alsoreferred to as atomic propositions, or predicates). An atomicproposition is a statement about the world that is either True or False.In such an example, a finite set of atomic propositions, AP, can be usedto indicate properties such as occupancy of a spatial region.Additionally, or in the alternative, a labeling function

:S→2″ map be provided as a map from system states to subsets of atomicpropositions that are True (e.g., with the rest being False).

In any example as stated above, a run of an MDP s=s₀s₁s₂ . . . can bedefined as an infinite sequence of state pairs, where s_(i)∈S is theagent state at time step i, and there is some action a∈A that, whenapplied from s_(i), can result in s_(i+1). Furthermore, a word can bedefined as an infinite sequence of labels

(s)=

(s₀)

(s₁)

(s₂) . . . , for some run s. Using such a notation, a suffix of sstarting at index, i, can be defined as s_(i)=s_(i) s_(i+1) s_(i+2) . .. , with corresponding word

(s_(i)).

LTL can be used to concisely and precisely specify permitted andprohibited system behaviors in terms of the corresponding words.Formulas in LTL are constructed from p∈AP according to a grammar:φ::=p|¬φ|φ∨φ|Xφ|φUφ  (8)

where is negation, ∨ is disjunction, X is “next”, and U is “until.”Boolean constants True and False are defined as usual: True=p∨¬p andFalse=¬True. Conjunction (∧), implication (⇒), equivalence (⇔),“eventually” (Fφ=True Uφ) and “always” (Gφ=¬F¬φ) are derived.

The semantics of LTL can be defined inductively over a word

(s) as follows:

$\begin{matrix}\begin{bmatrix}{\mathcal{L}\left( s_{i} \right)} & \vDash & {{p\mspace{14mu}{if}\mspace{14mu}{and}\mspace{14mu}{only}\mspace{14mu}{if}\mspace{14mu} p} \in {\mathcal{L}\left( s_{i} \right)}} \\{\mathcal{L}\left( s_{i} \right)} & \vDash & {{⫬ {\varphi\mspace{14mu}{if}\mspace{14mu}{and}\mspace{14mu}{only}\mspace{14mu}{if}\mspace{14mu}{\mathcal{L}\left( s_{i} \right)}}} \vDash \varphi} \\{\mathcal{L}\left( s_{i} \right)} & \vDash & {{{\varphi_{1}\bigvee\varphi_{2}}\mspace{14mu}{if}\mspace{14mu}{and}\mspace{14mu}{only}\mspace{14mu}{if}\mspace{14mu}{\mathcal{L}\left( s_{i} \right)}} \vDash \varphi_{1}} \\\; & \; & {{{and}\mspace{14mu}{\mathcal{L}\left( s_{i} \right)}} \vDash \varphi_{2}} \\{\mathcal{L}\left( s_{i} \right)} & \vDash & {{X\;\varphi\mspace{14mu}{if}\mspace{14mu}{and}\mspace{14mu}{only}\mspace{14mu}{if}\mspace{14mu}{\mathcal{L}\left( s_{i + 1} \right)}} \vDash \varphi} \\{\mathcal{L}\left( s_{i} \right)} & \vDash & {\varphi_{1}U\;\varphi_{2}\mspace{14mu}{if}\mspace{14mu}{and}\mspace{14mu}{only}\mspace{14mu}{if}\mspace{14mu}{\exists{j \geq {i\mspace{14mu}{such}\mspace{14mu}{that}}}}} \\\; & \; & {{{\mathcal{L}\left( s_{j} \right)} \vDash {\varphi_{2}\mspace{14mu}{and}\mspace{14mu}{\forall\left. {i \leq k}\leftarrow j \right.}}},{{\mathcal{L}\left( s_{k} \right)} \vDash \varphi_{1}}}\end{bmatrix} & (9)\end{matrix}$

A word

(s) satisfies φ, denoted by

(s)

φ, if

(sx₀)

φ. A run s satisfies φ if

(s)

φ.

In such a system, Xφ expresses that φ is true in a subsequent “step” orposition in the run's state sequence (e.g., neXt), φ_(i)Uφ₂ expressesthat φ_(i) is true until φ₂ becomes true (e.g., Until), Gφ means that φis true in every position (e.g., Globally true), Fφ means φ is true atsome position (e.g., Finally), GFφ means φ is true infinitely often (itreoccurs indefinitely), and aRb expresses that b holds indefinitelyuntil a becomes true (e.g., Release). Importantly, in some examples,changes in atomic propositions can be described over time.

In general, it is possible to define two primary types of propertiesallowed in a specification: safety properties, which guarantee that“something bad never happens”, and liveness conditions, which state that“something good (eventually) happens.” Such types correspond naturallyto LTL formulas with operators “always” (G) and “eventually” (F), asdiscussed above.

Turning to the automata 216 discussed above, in some examples, suchlogical expressions (e.g., the TL formula 214) can be formulated asdeterministic Rabin automata (DRA). A deterministic Rabin automaton is atuple

=(Q,Σ,δ,q₀,F) comprising: a finite set of states Q, a finite alphabet Σ,a transition function δ: Q→Q, an initial state q₀ ∈Q, and a set ofaccepting pairs Ω={(L₁,U₁), . . . , (L_(N),U_(N))}. Such automata havean equivalence with LTL formulas. As described briefly below, any LTLformula can be translated into one of the automata 216.

As a non-limiting example, let E′ be the set of infinite words over Σ. Arun of

can be defined as an infinite sequence q₀q₁q₂ . . . of states in

such that there exists a word σ=σ₀σ₁σ₂ . . . ∈Σ^(ω) with(q₁,σ_(i))=q_(i+1) for i≥0. Run q₀q₁q₂ . . . can be defined to beaccepted by

if there is a pair (L_(j),U_(j))∈Ω such that q_(i)∈L_(j) for infinitelymany indices i∈

and q_(i)∈U_(j) for at most finitely many i.

As such, it is possible to denote by

(

) the set of words that are accepted by

. Any LTL formula φ over variables in AP can, therefore, beautomatically translated into a corresponding DRA

_(φ), of size automaton 2^(2|AP|) such that σ∈

(

_(φ))⇔σ

φ.

Using either an LTL formulation, or DRA, such statements or formula cancorrespond, for example, to the output of sensors and processors onboardan autonomous vehicle. For example, various LIDAR, RADAR, cameras,ultrasonic transducers, and the like can return sensor data. Such sensordata can be subject to various algorithms, such as blob detectors,object detectors, object classifiers, to determine the presence (orabsence of) objects in an environment, as well as object properties(e.g., size, shape, orientation, position, velocities, etc.). Similarsensor modalities can be employed to localize such an autonomous vehiclein a 3D map by the use of, for example, Kalman filters, particlefilters, bundle adjustment, SLAM (simultaneous localization and mapping)algorithms in general, or the like. As a particular example, an LTLformula can be evaluated as true once an autonomous vehicle hasdetermined that it has approached an intersection, detected anothervehicle at the intersection, and waited until there was no longeranother vehicle in the intersection.

Turning to the tree search module 224 discussed above, in some examples,searching for a policy can be performed using a sampling-basedalgorithm, such as a Monte Carlo Tree Search (MCTS). A MCTS can beconsidered to be a general heuristic search algorithm that forms thebasis of a large family of game-playing algorithms. Such an algorithmcan be performed on discrete sets of data, as well as in continuousdomains by incorporating various modifications. In various examples, anUpper Confidence Bound (UCB) for Trees version of the MCTS can be used.

In such an example, the tree is recursively descended, starting withs=s₀ as the current state. During descent, at each branch the UCB metriccan be used to choose an action. The UCB metric can be defined as:

$\begin{matrix}\left\lbrack {a^{*} = {{\arg\;{\max_{a}{Q\left( {s,a} \right)}}} + {C\sqrt{\frac{\log\;\left( n_{a} \right)}{n_{s} + 1}}}}} \right\rbrack & (10)\end{matrix}$

In those instances where an unexplored node is reached, a rollout tosimulate a value of the node can be performed until a horizon or aterminal state for the current problem is reached.

In some examples, system evolution can be determined as a function ofboth continuous and discrete dynamics. For example, evolution of acontinuous state and a discrete state can be defined as:[x′=f_(c)(x,w,u,o), w′=f_(d) (x,w,u,o)], wherex∈X⊆

^(n) ^(c) is the continuous state,  (11)u∈U⊆

^(m) ^(c) is the continuous control input,  (12)w∈W is the discrete (logical) world state, and  (13)o∈O is a discrete (logical) option from a finite set O.  (14)

As such, atomic propositions p∈AP can be defined as functions over thediscrete world state, for example, as p: W→{True, False}.

In the MDP framework, S=X×W, A=U×O, δ(xw,uo)=x′w′ such thatx′=f_(c)(x,w,u,o),w′=f_(d)(x,w,u,o). In such a framework, the labelingfunction over states can be represented as:

(xw)={p∈AP such that p(w)=True}  (15)

In some examples, such a system can be decomposed into actors. Forexample, each independent entity can be an actor. Additionally, or inthe alternative, the agent under control (e.g., the autonomous vehicle)can be considered to be an actor. In those examples comprising multipleactors, a world state s=xw∈X×W can comprise an environment, e∈ε and somenumber of actors, N. Using such a definition, the i-th world state in asequence can be fully defined as: [x_(i)w_(i)=

x_(0,i)w_(0,i), x_(1,i)w_(1,i), . . . , x_(N,i)w_(N,i), e

], where each actor k's state x_(k,i)∈

^(n) ^(k,c) and w_(k,i)∈W_(k) such that Σ_(k)n_(k,c)=n_(c) and ΠW_(k)=W.In such an example, actor 0 can be designated a planner for theautonomous system.

Using this decomposition, it is possible to use a feature functionφ:S→F, which computes a low-dimensional representation of the worldstate containing all information needed to compute a policy. As anon-limiting example, the problem can be decomposed into finding twosets of policies: a policy π_(O):F→O over high-level actions and apolicy π_(U):O×F→U over low-level controls, such that their compositionsolves the MDP. In such an example, a first subgoal can be to compute apolicy π_(U)*(·,o) for each high-level option, o, that maps fromarbitrary feature values to controls:[π_(U)*(φ(xw),o)=argmax_(u)(V*(δ(xw,uo)))]  (16)

Additionally, or in the alternative, a second policy over options, m canbe computed:[π_(O)*(φ(xw))=argmax_(o)π_(U)*(φ(xw),o)]  (17)

Because of additional structure imposed on the final policy (which takesthe form π*(s)=π_(U)*(φ(s),π_(o)*(s))), the optimal policy found will bethat based on the set of options O (e.g., which can not necessarily bethe true optimal policy).

As briefly indicated above (and with respect to any of FIGS. 1-9),creating a control algorithm for an autonomous vehicle can beaccomplished by a mixture of discrete and continuous spaces. Byincorporating logical statements with a sampling based algorithm,low-level policies and high-level policies can be decomposed andcombined to provide insight into actions to perform. In some examples,learned policies can be used together with an approach based on MonteCarlo Tree Search (MCTS). Such learned policies can be based on variousmachine learning algorithms. Machine learning generally refers to abroad class of such algorithms in which an output is generated based onlearned parameters, which will be discussed in detail below. In someexamples, as briefly mentioned above, one machine learning algorithmwhich can be used is a deep neural network.

In some examples, learning models are simple multilayer perceptrons with32 hidden neurons, though more or less can be used. Additionally, or inthe alternative, models may be trained using Keras and TensorFlow. Insome examples, the Keras-RL implementations of deep reinforcementlearning algorithms DQN (Deep Q-Networks), DDPG (Deep DeterministicPolicy Gradients), and continuous DQN can be used.

In those examples which employ an Upper Bound Confidence, the UpperConfidence Bound (UCB) weight term can be set as follows:

$\begin{matrix}\left\lbrack {{Q\left( {w_{i},o_{i}} \right)} + {C\;\frac{P\left( {w_{i},o_{i}} \right)}{1 + {N\left( {w_{i},o_{i}} \right)}}}} \right\rbrack & (18)\end{matrix}$where C is an experimentally-determined, domain-specific constant.

In those examples which use this term, exploration is encouraged whilefocusing on option choices that performed well according to previousexperience. As such, a high weight can be granted to any terms that havea high prior probability from the learned model.

Additionally, or in the alternative, a Progressive Widening can be usedto determine when to add a new node to the MCTS. In some examples, aversion of MCTS with Progressive Widening that searches over learnedoptions can be used. In those examples, Progressive Widening can beimplemented as n_(children)=√{square root over ((n_(w)))}. In someinstances, the third, fourth, fifth-roots, etc., can be used forProgressive Widening, and is not necessarily limited to the user of thesquare root.

In some instances, the MCTS can utilize any machine learning algorithmsor neural networks. In addition to or in the alternative to the examplediscussed herein, one example of a neural network can include aconvolutional neural network, or CNN. Each layer in a CNN can alsocomprise another CNN, or can comprise any number of layers. As can beunderstood in the context of this disclosure, a neural network canutilize machine learning, which can refer to a broad class of suchalgorithms in which an output is generated based on learned parameters.

Although discussed in the context of neural networks, any type ofmachine learning can be used consistent with this disclosure. Forexample, machine learning algorithms can include, but are not limitedto, regression algorithms (e.g., ordinary least squares regression(OLSR), linear regression, logistic regression, stepwise regression,multivariate adaptive regression splines (MARS), locally estimatedscatterplot smoothing (LOESS)), instance-based algorithms (e.g., ridgeregression, least absolute shrinkage and selection operator (LASSO),elastic net, least-angle regression (LARS)), decisions tree algorithms(e.g., classification and regression tree (CART), iterative dichotomiser3 (ID3), Chi-squared automatic interaction detection (CHAID), decisionstump, conditional decision trees), Bayesian algorithms (e.g., naïveBayes, Gaussian naïve Bayes, multinomial naïve Bayes, averageone-dependence estimators (AODE), Bayesian belief network (BNN),Bayesian networks), clustering algorithms (e.g., k-means, k-medians,expectation maximization (EM), hierarchical clustering), associationrule learning algorithms (e.g., perceptron, back-propagation, hopfieldnetwork, Radial Basis Function Network (RBFN)), deep learning algorithms(e.g., Deep Boltzmann Machine (DBM), Deep Belief Networks (DBN),Convolutional Neural Network (CNN), Stacked Auto-Encoders),Dimensionality Reduction Algorithms (e.g., Principal Component Analysis(PCA), Principal Component Regression (PCR), Partial Least SquaresRegression (PLSR), Sammon Mapping, Multidimensional Scaling (MDS),Projection Pursuit, Linear Discriminant Analysis (LDA), MixtureDiscriminant Analysis (MDA), Quadratic Discriminant Analysis (QDA),Flexible Discriminant Analysis (FDA)), Ensemble Algorithms (e.g.,Boosting, Bootstrapped Aggregation (Bagging), AdaBoost, StackedGeneralization (blending), Gradient Boosting Machines (GBM), GradientBoosted Regression Trees (GBRT), Random Forest), SVM (support vectormachine), supervised learning, unsupervised learning, semi-supervisedlearning, etc.

In some examples, it can be possible to check the model, which is tosay, it can be possible to evaluate a correctness of varioustrajectories using the TL formula 214 discussed above. As a non-limitingexample, each discrete option can be associated with an LTL formulaφ_(o) which establishes preconditions for applying that option. In thoseexamples, a query can be performed u_(i)=π_(U)(o,φ(x_(i)w_(i))) to getthe next control as long as φ_(o) holds. Additionally, or in thealternative, a shared set Φ of LTL formulas can be selected thatconstrain the entire planning problem.

In some examples, in order to evaluate the cost function when learningoptions, as well as during MCTS, it is possible to check whether sampledruns satisfy an LTL formula (e.g., the TL formula 214). For example,given an infinite run s, one method to determining if

(s)

φ is to check whether

(s) is in the language of the Deterministic Rabin Automaton (DRA) thatrecognizes φ. In such an example, checking that an infinite run ssatisfies φ is equivalent to checking if

(s)∈

(

_(p)). However, when checking finite runs, all possible infinitesuffixes must be evaluated when defining the bounded-time semantics.

In some examples, a finite run prefix, s_(pre)=s₀s₁ . . . s_(i), can bedetermined to satisfy φ, denoted s_(pre)

_(i)φ, if for all possible suffixes s_(suff)=s_(i+1)s_(i+2) . . . ,s_(pre)s_(suff)

φ. Conversely, s_(pre)=s₀s₁ . . . s_(i) violates φ, denoted s_(pre)

φ, if for all possible suffixes s_(suff)=s_(i+1)s_(i+2) . . . ,s_(pre)s_(suff)

φ. If there are suffixes that satisfy as well as violate φ, then it isnot possible to make a determination about s_(pre)'s satisfaction of φ.

In some examples, model checking is performed using the above boundedsemantics. In those models, the state of the DRA

_(φ) (e.g., the automata 216) can be partitioned into accepting (A),rejecting (R), and neutral states (N). Further, each state can belabeled, q, based on an existence of Rabin suffixes that begin in q andsatisfy an acceptance condition. Such a pre-computation can be doneusing Tarjan's algorithm for strongly connected components (SCCs). Inthose examples which use such an algorithm, all A and R states arecontained in Bottom SCCs, e.g., SCCs that are sinks. In those exampleswhich use an annotated DRA, checking that a finite prefix s_(pre)

_(i)φ can be done in O(i) time.

FIG. 3 depicts an example scenario 300 including an autonomous vehiclenavigating a stop sign. In this scenario 300, an environment 302includes an autonomous vehicle 304 driving on a road toward a stop sign306. In one example, to complete this task, the autonomous vehicle 304must approach the stop sign 306, stop in a stop region 308 before a stopline 310, wait, and accelerate away from the stop sign 306 to continuetowards another goal. As can be understood, the scenario 300 can be aportion of a larger task or trajectory (e.g., to travel from onelocation to another location). As illustrated, the stop region 308 canbe associated with a front 312 and a back 314, which can be explained inconnection with a context 316.

As discussed above, the stop region 308 can be a static symboldetermined by the static symbol scanning module 202 of the decisionmodule 106. In some instances, other objects such as the front 312 andthe back 314 of the stop region 308, the stop line 310, and the stopsign 306 can be static symbols as well. In some instances, the staticsymbols can be encoded into a map (e.g., the map(s) 136), and in someinstances, the static symbols can be determined by a perception systemusing image segmentation and/or classification. As the static symbolsare encountered within a horizon of the autonomous vehicle 304, thestatic symbols can be instantiated in the context 316, which can store astate of the world represented in the environment 302. In someinstances, the autonomous vehicle 304 can be considered as a static ordynamic symbol.

Thus, the context 316 can include symbols(s) 318, including but notlimited to, the autonomous vehicle: AV and the StopRegion: SR. Ofcourse, the context 316 can include any number of the symbols 318depending on a complexity of the environment 302 in which the autonomousvehicle 304 is operating. Further, the context 316 can depend on ahorizon associated with the decision module 106. Of course, as a size ofthe horizon increases (e.g., to 50 meters, 100 meters, 200 meters,etc.), a number of symbols 318 within the horizon can increase, therebyincreasing a complexity of the decision-making process. In someinstances, a size of the horizon can depend on a velocity of theautonomous vehicle 304 (e.g., as velocity increases a size of thehorizon increases). In some instances, a size of a horizon can increaseuntil a threshold number of symbols are detected (e.g., expanding thehorizon until 10 symbols are determined).

As the symbols 318 are added to the context 316, the operations caninclude automatically populating the context 316 with correspondingfeatures 320, predicates 322, and LTL formula 324. As can be understood,the various features 320, predicates 322, and the LTL formula 324 can beselected from the corresponding libraries 218, 220, and 222 of FIG. 2,respectively.

Turning to the features 320, the features 320 can include, but are notlimited to features including AVDistanceSRFront(AV, SR), andAVDistanceSRBack(AV, SR). By way of example, the featureAVDistanceSRFront(AV, SR) depends of a state of the autonomous vehicle(AV) 304 and the stop region (SR) 308, and returns a numerical valueindicating a distance between the front of the stop region (312) and theautonomous vehicle 304. Similarly, the feature AVDistanceSRBack(AV, SR)depends of a state of the autonomous vehicle (AV) 304 and the stopregion (SR) 308, and returns a numerical value indicating a distancebetween the back of the stop region (314) and the autonomous vehicle304. In some examples, a front portion of the autonomous vehicle 304 canbe used when determining distances of the example features 320 discussedabove, although any point associated with the autonomous vehicle 304 canbe used as well.

As the features 320 are instantiated into the context 316, thepredicates 322 can be automatically added to the context 322 as wellbased on the presence of the symbols 318 and the features 320. In thescenario 300, exemplary predicates can include, but are not limited to:AVZeroSpeed(AV), which evaluates as True or False depending on whetherthe autonomous vehicle 304 is stopped or not;AVInSR(AVDistanceSRFront(AV, SR), AVDistanceSRBack(AV, SR)), whichevaluates as True or False depending on whether the autonomous vehicle(AV) 304 is in the stop region (SR) 308, and can be based on thefeatures discussed above (e.g., AVDistanceSRFront(AV, SR) andAVDistanceSRBack(AV, SR)); SRAheadOfAV(AVDistanceSRFront(AV, SR)), whichevaluates as True or False depending on whether the stop region (SR) 308is ahead of the autonomous vehicle (AV) 304, and depends on the featureAVDistanceSRFront(AV, SR); and SRBehindAV(AVDistanceSRBack(AV, SR)),which evaluates as True or False depending on whether the stop region(SR) 308 is behind the autonomous vehicle (AV) 304, and can depend onthe feature AVDistanceSRBack(AV, SR).

As the predicates 322 are instantiated into the context 316, the LTLformula 324 can be automatically added to the context 316 based on thepresence of the symbols 318, the features 320, and the predicates 322.For example, in this scenario 300, the applicable LTL formula 324 caninclude:G(SRAheadOfAV⇒(¬SRBehindAVU(AVInSR∧AVZeroSpeed)))  (19)

The equation above can correspond to a statement read as: “Globally (atany point in a trajectory), if the autonomous vehicle (e.g., 304) sees astop region (e.g., 308) ahead of the autonomous vehicle (e.g., 304),then it should not be the case that stop region (e.g., 308) is behindthe autonomous vehicle (e.g., 304) until the autonomous vehicle (e.g.,304) has stopped in the stop region (e.g., 308).” For example, atrajectory that did not stop in the stop region 308 would violate thisLTL formula 324 because the stop region 308 would be behind theautonomous vehicle 304 without the autonomous vehicle 304 stopping inthe stop region 308.

In some instances, the LTL formula 324 can be used to generate one ormore automaton, which can be used in model checking or verifying thatvarious trajectories comply with the LTL formula 324. For example, thecontext 316 can be incorporated into a Monte Carlo Search Tree (MCTS)and a state of the context 316 can be evolved forward as varioussnapshots to create various candidate trajectories. Further, candidatetrajectories can be evaluated against various LTL formula to determineif the trajectories violate the formulas. If a trajectory violates aformula, trajectory can be discarded as part of the search. For example,the statement “car in intersection implies intersection is clear and(the car was not in the intersection until the car had a higher prioritythan other vehicles)” is an LTL constraint that corresponds to acondition of a vehicle waiting for its turn at a four way stop.

Accordingly, various trajectories can be generated and checked againstthe LTL formula 324 and/or against one or more automaton correspondingto the LTL formula 324 to verify a correctness of individualtrajectories. In some instances, if different trajectories do notviolate the LTL formula 324 (e.g., more than one trajectory satisfiesthe LTL formula 324), a trajectory can be selected based on costs (e.g.,speed, comfort, performance, etc.). For example, costs can be determinedand associated with specific actions associated with a trajectory. Inone example, a first trajectory may satisfy the LTL formula associatedwith a task and may have a low cost relative to a second trajectory thatalso satisfies the LTL formula but has a higher cost to complete thetrajectory. The decision module 106 may select the first trajectory toguide the autonomous vehicle 304, as the lower cost of the firsttrajectory may represent a faster travel, more comfortable ride (e.g.,comfortable accelerations and decelerations), or may represent reducedwear and tear on the autonomous vehicle 304, for example.

FIG. 4 depicts an example scenario 400 including an autonomous vehiclenavigating a three-way intersection. In this scenario 400, anenvironment 402 includes an autonomous vehicle 404 driving on a roadtowards an intersection which is partially controlled by a yield sign406. In this scenario, a high-level goal for the autonomous vehicle 404is to approach the intersection and turn left. The yield sign 406 canhave an associated yield line 408 and a yield region 410, and theintersection can include a turn region 412 and a post turn region 414.As discussed above, the static features in the environment 402 can bedetermined as a static symbol from a map, or determined via a perceptionsystem of the autonomous vehicle 404.

The environment 402 also includes vehicles 416 and 418, which can bedetermined by a perception system or prediction system of the autonomousvehicle 404. Further, the first vehicle, V₁ 416, can have an associatedapproach region ApproachOncoming 420, which can correspond to a regionof the road in which the vehicle 416 can be predicted to traverse. Thesecond vehicle, V₂ 418, can have an associated approach regionApproachInLane 422, which can correspond to a region in a lane in whichthe autonomous vehicle 404 can turn to accomplish a goal (e.g., turnleft at the intersection). In some instances, the regionsApproachOncoming 420 and ApproachInLane 422 can include a velocitycomponent that are based on a velocity of vehicles 416 and 418,respectively, which corresponds to a minimum stopping distance to stopto avoid a collision in the turn region 412. For example, the firstvehicle V₁ 416 can be traveling a first speed, such that theApproachOncoming 420 region represents a minimum stopping distance forthe vehicle 416 to stop if the autonomous vehicle 404 enters the turnregion 412 and is positioned in a region where a collision with thevehicle V₁ 416 would be possible. In other words, if the vehicle 416 isin the ApproachOncoming 420 region, the vehicle 416 cannot stop in theApproachOncoming 420 region (e.g., without traversing through the entireApproachOncoming 420 region) based on a velocity of the vehicle 416.

Based on the symbols present in the environment 402, a context 424 canbe populated including the various symbols 426, features 428, predicates430, and LTL formula 432 that are situationally relevant.

By way of example, and without limitation, the symbols 426 for theenvironment 402 can include: the turning region (TR 412); the post turnregion (PT 414); the yield region (YR 410); the ApproachOncoming 420region; the ApproachInLane 422 region; the first vehicle (V₁ 416); thesecond vehicle (V₂ 418); and the autonomous vehicle (AV 404).

By way of example, the features 428 can include various operationsrelated to a front and back of each of the regions 410, 412, 414, 420,and 422. These features 428 can be similar to the features discussedabove in connection with FIG. 3, although the details are omitted forsimplicity.

The predicates 430 can be included in the context 424 based on thesymbols 426 discussed above. By way of example, and without limitation,the predicates 430 can include: In(AV, YR), which evaluates as True orFalse depending on whether the autonomous vehicle 404 is in the yieldregion 410; In(AV, TR), which evaluates as True or False depending onwhether the autonomous vehicle 404 is in the turn region 412; In(AV,PT), which evaluates as True or False depending on whether theautonomous vehicle 404 is in the post turn region 414; In(V_(i),ApproachOncoming), which evaluates as True or False depending on whethera vehicle (e.g., V₁ 416 or V₂ 418) is in the ApproachOncoming 420region; In(V₁, ApproachInLane), which evaluates as True or Falsedepending on whether a vehicle (e.g., V₁ 416 or V₂ 418) is in theApproachInLane 422 region; In(V_(i), TR), which evaluates as True orFalse depending on whether a vehicle (e.g., V₁ 416 or V₂ 418) is in theturn region 412; Cutoff(V_(i), TR), which evaluates as True or Falsedepending on whether a vehicle (e.g., V₁ 416 or V₂ 418) would need toslam on their brakes to avoid collision if there is an object in theturn region 412; Clear(TR), which evaluates as True or False based onthe predicates In(V₁, TR), In(V₁, ApproachOncoming), In(V_(i),ApproachInLane), and Cutoff(V₁, TR); Stopped(AV), which evaluates asTrue or False based on whether the autonomous vehicle 404 is stopped;and Collision(AV, V_(i)), which evaluates as True or False based onwhether the autonomous vehicle 404 has collided with one of the vehiclesV₁ 416 or V₂ 418.

Similarly, the LTL formulas 432 can be added to the context 424 as thesymbols 426, the features 428, and the predicates 430 are instantiated.By way of example, and without limitation, exemplary LTL formulas 432include:¬Clear U(∧_(i)¬In(V _(i),TR)∧_(i)¬In(V _(i),ApproachOncoming)∧_(i)¬In(V _(i),ApproachInLane))  (20)

The equation (20) can be understood by the following statement: “It isnot clear (e.g., for the autonomous vehicle 404 to make a turn) until novehicles (e.g., V₁ 416 and V₂ 418) are in the turn region 412 andapproach regions 420 and 422.”G(In(AV,YR)⇒(In(AV,YR)U Clear(TR)))  (21)

The equation (21) can be understood by the following statement: “Stay inthe yield region 410 until the turn region 412 is clear.”G(In(AV,TR)⇒¬Stopped(AV))  (22)

The equation (22) can be understood by the following statement: “Nostopping in the turn region 412.”G(In(AV,TR))⇒F(In(AV,PT))  (23)

The equation (23) can be understood by the following statement: “Theautonomous vehicle 404 being in the turn region 410 implies eventuallymaking it to the post turn region 414.”¬F(Collision(H,V _(i)))  (24)

The equation (24) can be understood by the following statement: “Theautonomous vehicle 404 should never collide with vehicles (e.g., V₁ 416and V₂ 418).”

Of course, the scenario 400 is one exemplary embodiment, and anenvironment can include any number of static symbols and/or dynamicsymbols, and accordingly, a context can have any variety ofsituationally relevant symbols, context, features, predicates, and LTLformula, as discussed herein.

FIG. 5 depicts an example scenario including an autonomous vehiclenavigating a four-way intersection. In this scenario 500, an environment502 includes an autonomous vehicle 504 driving on a road towards afour-way intersection controlled by stop signs 506, 508, 510, and 512.In this scenario, a high-level goal for the autonomous vehicle 504 is toapproach the intersection, stop, wait for right of way, and travelthrough the intersection. Each of the stop signs 506, 508, 510, and 512can have an associated stop line (illustrated in FIG. 5) and associatedstop regions 514, 516, 518, and 520, and the intersection can include anintersection region 522, and an intersection path region 524. A lanegoal region 526 can correspond to the goal of the autonomous vehicle 504following traversal of the intersection. The environment 502 can includevehicles V₁ 528 and V₂ 530. As discussed above, the static features inthe environment 502 can be determined as a static symbol from a map, ordetermined via a perception system of the autonomous vehicle 504, whilethe dynamic symbols can be determined via the perception system.

As indicated in FIG. 5 by the arrows associated with the vehicles V₁ 528and V₂ 530 (and as indicated throughout the disclosure), the vehicles V₁528 and V₂ 530 can be traveling towards the stop signs 512 and 508,respectively. In some instances, a prediction system of the autonomousvehicle 504 can be monitoring the motion of the vehicles V₁ 528 and V₂530 to determine or anticipate when the vehicles V₁ 528 and V₂ 530 willarrive at the stop regions 520 and 516, respectively, and can base theplanning of the autonomous vehicle 504 at least in part on the predictedtrajectories of the vehicles V₁ 528 and V₂ 530.

Based on the symbols present in the environment 502, a context 532 canbe populated including the various symbols 534, features 536, predicates538, and LTL formula 540 that are situationally relevant.

By way of example, and without limitation, the symbols 534 for theenvironment 502 can include: the intersection region (I 522); the lanegoal region (L 526); the intersection path region (P 524); the stopregions (SR₁ 514, SR₂ 516, SR₃ 518, and SR₄ 520); the autonomous vehicle(AV 504), and the vehicles (V₁ 528 and V₂ 530).

By way of example, the features 536 can include various operationsrelated to a front and back of each of the regions 514, 516, 518, 520,522, and 524. These features 536 can be similar to the featuresdiscussed above in connection with FIG. 3, although the details areomitted for simplicity.

The predicates 538 can be included in the context 532 based on thesymbols 534 discussed above. By way of example, and without limitation,the predicates 538 can include: In(AV, I), which evaluates as True orFalse depending on whether the autonomous vehicle 504 is in theintersection region 522; In(AV, L), In(AV, P), In(AV, SR_(i)), In(V_(i),I), In(V_(i), SR_(i)), which individually evaluate as True or Falsedepending on whether the subject vehicle (e.g., AV 504, V₁ 528, V₂ 530)is in the subject region (e.g., L 526, P 524, SR₁ 514, SR₂ 516, SR₃ 518,SR₄ 520, and I 522); AVTurn(AV, V_(i), SR_(i)), which can be representedas a logical formula that evaluates as True or False depending onwhether the various vehicles are in various regions, and based on ahistory to determine if it is time for the autonomous vehicle 504 to go(e.g., based on whether the autonomous vehicle 504 has the right ofway); Clear(I), which can be represented as a logical formula based onIn(V_(i), I) to determine if the intersection region 522 is clear;Stopped(AV); and HasStopped(AV, SR₁), which evaluates as True or Falsedepending on whether the autonomous vehicle 504 previously came to astop in the stop region SR′ 514.

Similarly, the LTL formulas 540 can be added to the context 532 as thesymbols 534, the features 536, and the predicates 538 are instantiated.By way of example, and without limitation, exemplary LTL formulas 540include:G(In(AV,SR₁))⇒(In(AV,SR₁)U(HasStopped(AV,SR₁)∧Clear(I)∧AVTurn(AV,V _(i),SR₁))))  (25)

The equation (25) can be understood by the following statement: “Theautonomous vehicle 504 is to stay in the stop region 514 until theautonomous vehicle 504 has come to a stop in the stop region 514, theintersection 522 is clear, and it is the turn of the autonomous vehicle514.”G(In(AV,P))⇒¬Stopped(AV)  (26)

The equation (26) can be understood by the following statement: “Nostopping in the intersection path region 524.”FIn(AV,L)  (27)

The equation (27) can be understood by the following statement: “Theautonomous vehicle will eventually reach the goal lane region 526.”

FIG. 6 illustrates a search tree 600 for evaluating candidatetrajectories, as described herein. In some instances, the search tree600 can be associated with a measured trace 602, which can storeobservations about the environment over time, such as the presence ofsymbols in an environment, states of an autonomous vehicle (e.g.,velocity, steering angle, acceleration, etc.). Further, the search tree600 can be associated with a current state 604, which can include asnapshot 606. In some examples, the snapshot 606 can represent a stateof an environment at a particular instant in time, and can include, butis not limited to, various symbol(s), feature(s), predicate(s), LTLformula(s), etc. In some instances, current state 604 can be consideredto be a part of the measured trace 602.

Based at least in part on the snapshot 606 reflecting the current state604 at T₀ (e.g., an initial time), the search tree 600 can evolve thesnapshot 606 over time, represented as a speculative trace 608, whichcan reflect speculations about the environment as various trajectoriesare considered for selection for the autonomous vehicle. In someexamples, the speculative trace 608 can include predictions about othervehicles (e.g., not controlled by the decision module 106) in theenvironment with the autonomous vehicle.

As illustrated, the search tree 600 can represent different states atdifferent times and/or based on different potential actions. Further, itcan be understood that the search tree 600 can represent speculation inthe future as the passage of time moves from left to right in FIG. 6, asrepresented by a timeline 610. Nodes have been labeled by time step andto distinguish between different speculative traces. For example, nodes612 and 614 represent speculative traces at time T₁, a time after T₀,but represent two different speculations, “A” and “B.” Thus, the node612 can be referred to as T_(1A), while the node 614 can be representedas T_(1B). In some instances, Progressive Widening can be used todetermine when to add a new node, which may limit a maximum number ofchildren of a given node based at least in part on a number of times aworld state has been considered or visited by the search algorithm. Insome instances, each action modeled in the search tree 600 has one ormore associated termination conditions. When the search tree 600 reachesa termination condition associated with an action (e.g., completion of alane change, traversing a section of road, passage of a period of time,movement above a threshold distance, threshold velocity, thresholdacceleration, etc.), the search tree 600 may branch and choose a newaction to follow. In some instances, a termination condition can be alogical combination of at least two termination conditions. The searchcan continue until a termination condition is reached for a trajectoryor route as they related to a goal, such as a destination.

Just as the node 604 represents the snapshot 606 at an initial time,subsequent nodes can each include a snapshot representing a state of anenvironment based on a potential trajectory and potential changes in theworld over time. For example, a node 616 can include a snapshot 620,while a node 618 can include a snapshot 622. As can be understood, thesnapshot 620 can be based on intervening updates and conditionsrepresented in the nodes T_(1A), T_(2A), and T_(3A), while the snapshot622 can be based on intervening updates and conditions represented inthe nodes T_(1B), T_(2B), and T_(3D).

Turning to the current state 604, various permutations of possibletrajectories can be modeled and stored as an instance of MCTS to besearched and compared against the LTL formulas and/or evaluated todetermine costs associated with various actions. For example, as theMCTS is built, a snapshot (e.g., representing the context or automata)can evolve the context based on changing conditions (e.g., over time, asobjects move, etc.), and the snapshot can be checked for compliance withthe various LTL formulas. If multiple trajectories are determined not toviolate an LTL formula, a trajectory with a lowest cost (or a highestperformance, comfort, etc.) can be selected. For example, for variousoperations of the autonomous vehicle, or for various possibletrajectories, a cost function can penalize acceleration, jerk, lateralacceleration, yaw, steering angle, steering angle rate, etc.

In some instances, machine learning can be used to more accuratelydetermine possible trajectories to investigate using the MCTS based on acurrent state and/or learned trajectories in response to the currentstate(s) and/or tasks to be completed. For example, based on a currentstate of an environment, the MCTS with machine learning can determinecandidate trajectories that are most likely to result in satisfactoryoutcomes based on learned low-level policies (e.g., how to travel in aroad lane, how to change lanes, how to stop, how not to tailgate, etc.)and learned high-level policies (e.g., previously selected actions withgood outcomes).

FIGS. 7 and 8 illustrate example processes in accordance withembodiments of the disclosure. These processes are illustrated aslogical flow graphs, each operation of which represents a sequence ofoperations that can be implemented in hardware, software, or acombination thereof. In the context of software, the operationsrepresent computer-executable instructions stored on one or morecomputer-readable storage media that, when executed by one or moreprocessors, perform the recited operations. Generally,computer-executable instructions include routines, programs, objects,components, data structures, and the like that perform particularfunctions or implement particular abstract data types. The order inwhich the operations are described is not intended to be construed as alimitation, and any number of the described operations can be combinedin any order and/or in parallel to implement the processes.

FIG. 7 depicts an example process 700 for generating a trajectory for anautonomous vehicle, as described herein. For example, some or all of theprocess 700 can be performed by one or more components in thearchitectures 100 or 200, or in the environment 900, as describedherein.

At operation 702, the process can include determining one or moresymbols present in an environment. In some examples, the symbols caninclude any number or combination of static symbols and dynamic symbols.In some examples, the symbols can be determined by checking map datathat stores information associated with static symbols. In someinstances, the operation 702 can include determining a location of theautonomous vehicle on a map, determining symbols that are within ahorizon (e.g., a threshold distance) of the autonomous vehicle, andpopulating a context with the symbols. In some instances, the operation702 can include determining static or dynamic symbols via a perceptionsystem that can receive sensor data (e.g., LIDAR data, RADAR data,acoustic data, camera data, etc.), perform segmentation on the sensordata, and perform classification on the data to identify the staticand/or dynamic objects. In some instances, the operation 702 can includereceiving prediction data about the dynamic symbols, such as a probabletrajectory of the dynamic object(s).

At operation 704, the process can include determining features based onthe symbols determined in the operation 702. As discussed herein,features can return a numerical value that can be based on symbols orother features. For example, if symbols such as an autonomous vehicleand another vehicle are added to the context, a feature can determine adistance between the autonomous vehicle and the other vehicle. Further,a feature can include determining an identifier of a stop region (e.g.,stop region #123, where any identifier can be used). As can beunderstood, a variety of features can be used based on the symbolspresent in an environment.

At operation 706, the process can include determining one or morepredicates based on the features. As discussed herein, in someinstances, predicates can include logical formulas based on symbols,features, or other predicates that evaluate as True or False based oninput values. In one example, a predicate can be evaluated to determinewhether or not an autonomous vehicle has stopped in a stop region. Inanother example, a predicate can provide an indication of how well thepredicate is satisfied by the conditions. For example, for a predicatethat determines whether an autonomous vehicle stops in a stop region, ina scenario where the autonomous vehicle stops 1 cm beyond the stopregion, the Boolean evaluation of the predicate would be False, althougha predicate that returns an indication of the degree of satisfaction canindicate a location where the autonomous vehicle stopped or a degree ofthe predicate violation, and/or can associate a penalty with thataction. In some instances, a penalty for stopping 1 cm outside a stopregion can be a minor penalty, but a penalty for stopping 1 meter beyondthe stop region can be a major penalty.

At operation 708, the process can include determining one or more lineartemporal logic (LTL) formulas based at least in part on the predicates.Such formulas may be a subset of LTL formulas stored in a data storewhich are relevant. In some instances, the selected LTL formulas can bedirectly or indirectly based on one or more symbols, features,predicates, or other LTL formula present in the context. Examples of theLTL formulas are provided above in connection with FIGS. 3, 4, and 5, aswell as throughout the disclosure.

At operation 710, the process can include determining automata based onthe LTL formula. In some examples, the automata can correspond to aDeterministic Rabin Automata. In some instances, the operation 710 caninclude converting the LTL formula to a corresponding automata, whichcan accept as inputs states of the world and can be evaluated todetermine if a potential trajectory violates the LTL determined herein.Examples of various automata can include, but are not limited to Rabinautomata, Streett automata, Büchi automata, Muller automata, etc. Insome instances, the automata can accept any number of finite inputs orinfinite inputs. In some instances, the automata can include any numberof finite states, or can include an infinite number of states. In someinstances, the automata can include deterministic, non-deterministic, oralternation automata. In some instances, the automata can includenondeterministic or deterministic finite state machines, deterministicpushdown automata, linear bounded automata, Turing machines,non-deterministic or deterministic Büchi automata, Rabin automata,Streett automata, Parity automata, Muller automata, etc.

At operation 712, the process can include generating one or moretrajectories. At operation 714, the operation can include searchingthrough the trajectories using Monte Carlo Tree Search (MCTS). In someinstances, trajectories can be determined as the Monte Carlo Tree Searchis built. In some instances, the trajectories can be generated andprovided to the MCTS. In some instances, the trajectories can representany possible trajectories based on drivable surfaces and symbols. Insome instances, the trajectories can be based at least in part on a goalfor an autonomous vehicle, which can include traveling from a high-levelorigination location to a high-level destination location. In someinstances, trajectories for an autonomous vehicle can depend onpredicted trajectories for other vehicles, rules of the road, physicalconstraints (e.g., acceleration, steering angles, breaking, etc.), etc.Further, in some instances, for each trajectory generated to further theautonomous vehicle towards a goal, the operations 712 and/or 714 caninclude generating a fallback trajectory that can stop the vehicle orotherwise alter a trajectory of the autonomous vehicle in events such asemergencies (e.g., imminent collision).

At operation 716, the process can include evaluating the trajectories inthe MCTS using the automata. For example, the automata determined in theoperation 710 can evaluate each trajectory at individual time steps overtime. If a trajectory violates the LTL corresponding to the automata,the operation 716 can provide a Boolean indication of the status, and/orcan provide a value corresponding to the degree of satisfying orviolating the LTL formula.

At operation 718, the process can include selecting a trajectory basedat least in part on the trajectory satisfying one or more LTL formulasand one or more cost functions. For example, if multiple trajectoriessatisfy (e.g., do not violate) the LTL formula, the operation 718 canselect a trajectory based on a cost or performance associated with thetrajectory. In some instances, costs can be based at least in part onefficiency, comfort, performance, etc. of the autonomous vehicle. Thus,the process 700 can output a trajectory that has a highest performanceand lowest cost to accomplish a goal associated with an autonomousvehicle.

FIG. 8 depicts another example process for generating a trajectory foran autonomous vehicle, as described herein. For example, some or all ofthe process 800 can be performed by one or more components in thearchitectures 100 or 200, or in the environment 900, as describedherein.

At operation 802, the process can include determining one or more staticsymbols and/or dynamic symbols in an environment. In some instances, theoperation 802 can be based at least in part on a horizon associated withan autonomous vehicle. That is, the operation 802 can includedetermining static symbols and dynamic symbols within a horizon, orthreshold distance, from the autonomous vehicle. As discussed herein, insome instances, the static symbols can be determined from stored mapdata, and in some instances, static symbols and dynamic symbols can bedetermined via a perception system or a prediction system associatedwith the autonomous vehicle.

At operation 804, the process can include generating a context of theenvironment based at least in part on the static symbols and/or thedynamic symbols. For example, the context can include a state of theenvironment at a particular instant in time. In some instances, thecontext can include symbols, features, predicates, and/or LTL formula,automata, snapshots, costs, constraints, etc., as discussed herein.

At operation 806, the process can include populating a Monte Carlo TreeSearch (MCTS) with candidate trajectories. For example, the operation806 can include receiving the context generated in the operation 804above, and establishing an initial state of the MCTS with the currentcontext. The operations can include evolving the context forward in timebased on a progression of behaviors of objects represented in thecontext. For example, evolving the context can include changingpositions of dynamic objects based on current or expected velocities. Insome instances, the operation 806 can include selecting betweenavailable actions to generate branches of the MCTS, whereby thedifferent branches can represent differing trajectories. In someinstances, the operation 806 can utilize a trained neural network todetermine which actions to pursue, based at least in part on the currentor initial context.

At operation 808, the process can include selecting a trajectory basedat least in part on one or more costs. In some instances, the operationcan include verifying that any candidate trajectory does not violate anLTL formula. Further, in some instances, a violation of an LTL formulamany not result in discarding the candidate trajectory, but can beconsidered as a penalty, and can be considered when choosing atrajectory. In some instances, costs can depend on comfort aspects(acceleration, braking levels, etc.), and in some instances, the costcan be depend on safety aspects, in which case, a cost can be higher orlower depending on the importance of the factor under consideration.

At operation 810, the process can include commanding an autonomousvehicle to follow the trajectory. The operation 810 can includegenerating a sequence of commands to command the autonomous vehicle todrive along the trajectory selected in the operation 808. In someinstances, the commands generated in the operation 810 can be relayed toa controller onboard the autonomous vehicle, such as the trajectorymodule 108, the execution module 116, etc., to control the autonomousvehicle to traverse the trajectory. Although discussed in the context ofan autonomous vehicle, the process 800, and the techniques and systemsdescribed herein, can be applied to a variety systems utilizing machinevision.

FIG. 9 illustrates an environment 900 in which the disclosures can beimplemented in whole or in part. The environment 900 depicts one or morecomputer systems 902 that comprise a storage 904, one or moreprocessor(s) 906, a memory 908, and an operating system 910. The storage904, the processor(s) 906, the memory 908, and the operating system 910can be communicatively coupled over a communication infrastructure 912.Optionally, the computer system(s) 902 can interact with a user, orenvironment, via input/output (I/O) device(s) 914, as well as one ormore other computer system(s) over a network 916, via the communicationinfrastructure 912. The operating system 910 can interact with othercomponents to control one or more applications 918.

In some instances, the computer system(s) 902 can correspond to thecomputer system(s) 102 and/or the vehicle computing device 114 describedabove with reference to FIG. 1. Further, the computer system(s) 902 canimplement any hardware and/or software to implement the modules 104,106, 108, and 110 to perform route and trajectory planning, as discussedherein.

The systems and methods described herein can be implemented in softwareor hardware or any combination thereof. The systems and methodsdescribed herein can be implemented using one or more computer system(s)which can or can not be physically or logically separate from eachother. The methods can be performed by components arranged as eitheron-premise hardware, on-premise virtual systems, or hosted-privateinstances. Additionally, various aspects of the methods described hereincan be combined or merged into other functions.

With reference to the computer system(s) illustrated in FIG. 9, aprocessor or computer system can be configured to particularly performsome or all of the methods described herein. In some embodiments, themethods can be partially or fully automated by one or more computers orprocessors. The systems and methods described herein can be implementedusing a combination of any of hardware, firmware and/or software. Thepresent systems and methods described herein (or any part(s) orfunction(s) thereof) can be implemented using hardware, software,firmware, or a combination thereof and can be implemented in one or morecomputer systems or other processing systems. In some embodiments, theillustrated system elements could be combined into a single hardwaredevice or separated into multiple hardware devices. If multiple hardwaredevices are used, the hardware devices could be physically locatedproximate to or remotely from each other. The embodiments of the methodsdescribed and illustrated are intended to be illustrative and not to belimiting. For example, some or all of the steps of the methods can becombined, rearranged, and/or omitted in different embodiments.

In one example embodiment, the systems and methods described herein canbe directed toward one or more computer systems capable of carrying outthe functionality described herein. Example computer system(s)s can be,but are not limited to, a personal computer (PC) system running anyoperating system such as, but not limited to, OS X™, iOS™, Linux™,Android™, and Microsoft™ Windows™ However, the systems and methodsdescribed herein can not be limited to these platforms. Instead, thesystems and methods described herein can be implemented on anyappropriate computer system running any appropriate operating system.Other components of the systems and methods described herein, such as,but not limited to, a computer system(s), a communications device,mobile phone, a smartphone, a telephony device, a telephone, a personaldigital assistant (PDA), a personal computer (PC), a handheld PC, aninteractive television (iTV), a digital video recorder (DVD), clientworkstations, thin clients, thick clients, proxy servers, networkcommunication servers, remote access devices, client computers, servercomputers, routers, web servers, data, media, audio, video, telephony orstreaming technology servers, etc., can also be implemented using acomputer system(s). Services can be provided on demand using, e.g., butnot limited to, an interactive television (iTV), a video on demandsystem (VOD), and via a digital video recorder (DVR), or other on demandviewing system.

The computer system(s) can include one or more processors. Theprocessor(s) can be connected to a communication infrastructure, such asbut not limited to, a communications bus, cross-over bar, or network,etc. The processes and processors need not be located at the samephysical locations. In other words, processes can be executed at one ormore geographically distant processors, over for example, a LAN or WANconnection. Computer system(s) can include a display interface that canforward graphics, text, and other data from the communicationinfrastructure for display on a display unit.

The computer system(s) can also include, but is not limited to, a mainmemory, random access memory (RAM), and a secondary memory, etc. Thesecondary memory can include, for example, a hard disk drive and/or aremovable storage drive, such as a compact disc drive CD-ROM, etc. Theremovable storage drive can read from and/or written to a removablestorage unit. As can be appreciated, the removable storage unit caninclude a computer usable storage medium having stored therein computersoftware and/or data. In some embodiments, a machine-accessible mediumcan refer to any storage device used for storing data accessible by acomputer. Examples of a machine-accessible medium can include, e.g., butnot limited to: a magnetic hard disk; a floppy disk; an optical disk,like a compact disc read-only memory (CD-ROM) or a digital versatiledisc (DVD); a magnetic tape; and/or a memory chip, etc.

The processor can also include, or be operatively coupled to communicatewith, one or more data storage devices for storing data. Such datastorage devices can include, as non-limiting examples, magnetic disks(including internal hard disks and removable disks), magneto-opticaldisks, optical disks, read-only memory, random access memory, and/orflash storage. Storage devices suitable for tangibly embodying computerprogram instructions and data can also include all forms of non-volatilememory, including, for example, semiconductor memory devices, such asEPROM, EEPROM, and flash memory devices; magnetic disks such as internalhard disks and removable disks; magneto-optical disks; and CD-ROM andDVD-ROM discs. The processor and the memory can be supplemented by, orincorporated in, ASICs (application-specific integrated circuits).

The computer system(s) can be in communication with a computerized datastorage system. The data storage system can include a non-relational orrelational data store, such as a MySQL™ or other relational database.Other physical and logical database types could be used. The data storecan be a database server, such as Microsoft SQL Server™, Oracle™, IBMDB2™, SQLITE™, or any other database software, relational or otherwise.The data store can store the information identifying syntactical tagsand any information required to operate on syntactical tags. In someembodiments, the processing system can use object-oriented programmingand can store data in objects. In these embodiments, the processingsystem can use an object-relational mapper (ORM) to store the dataobjects in a relational database. The systems and methods describedherein can be implemented using any number of physical data models. Inone example embodiment, a relational database management system (RDBMS)can be used. In those embodiments, tables in the RDBMS can includecolumns that represent coordinates. In the case of economic systems,data representing companies, products, etc. can be stored in tables inthe RDBMS. The tables can have pre-defined relationships between them.The tables can also have adjuncts associated with the coordinates.

In alternative example embodiments, secondary memory can include othersimilar devices for allowing computer programs or other instructions tobe loaded into computer system. Such devices can include, for example, aremovable storage unit and an interface. Examples of such can include aprogram cartridge and cartridge interface (such as, e.g., but notlimited to, those found in video game devices), a removable memory chip(such as, e.g., but not limited to, an erasable programmable read onlymemory (EPROM), or programmable read only memory (PROM) and associatedsocket), and other removable storage units and interfaces, which canallow software and data to be transferred from the removable storageunit to computer system.

The computer system(s) can also include an input device such as, but notlimited to, a voice input device, such as a microphone, touch screens,gesture recognition devices, such as cameras, other natural userinterfaces, a mouse or other pointing device such as a digitizer, and akeyboard or other data entry device. The computer system(s) can alsoinclude output devices, such as but not limited to, a display, and adisplay interface. The computer system(s) can include input/output (I/O)devices such as but not limited to a communications interface, cable andcommunications path, etc. These devices can include, but are not limitedto, a network interface card, and modems. Communications interface(s)can allow software and data to be transferred between a computer systemand one or more external devices.

In one or more embodiments, the computer system(s) can be operativelycoupled to an automotive system. Such automotive system can be eithermanually operated, semi-autonomous, or fully autonomous. In such anembodiment, input and output devices can include one or more imagecapture devices, controllers, microcontrollers, and/or other processorsto control automotive functions such as, but not limited to,acceleration, braking, and steering. Further, communicationinfrastructure in such embodiments can also include a Controller AreaNetwork (CAN) bus.

In one or more embodiments, the computer system(s) can be operativelycoupled to any machine vision based system. For example, such machinebased vision systems include but are not limited to manually operated,semi-autonomous, or fully autonomous industrial or agricultural robots,household robot, inspection system, security system, etc. That is, theembodiments described herein are not limited to one particular contextand can be applicable to any application utilizing machine vision.

In one or more embodiments, the present embodiments can be practiced inthe environment of a computer network or networks. The network caninclude a private network, or a public network (for example theInternet, as described below), or a combination of both. The network caninclude hardware, software, or a combination of both.

From a telecommunications-oriented view, the network can be described asa set of hardware nodes interconnected by a communications facility,with one or more processes (hardware, software, or a combinationthereof) functioning at each such node. The processes caninter-communicate and exchange information with one another viacommunication pathways between them using interprocess communicationpathways. On these pathways, appropriate communications protocols areused.

An example computer and/or telecommunications network environment inaccordance with the present embodiments can include nodes, which caninclude hardware, software, or a combination of hardware and software.The nodes can be interconnected via a communications network. Each nodecan include one or more processes, executable by processors incorporatedinto the nodes. A single process can be run by multiple processors, ormultiple processes can be run by a single processor, for example.Additionally, each of the nodes can provide an interface point betweennetwork and the outside world, and can incorporate a collection ofsub-networks.

In an example embodiment, the processes can communicate with one anotherthrough interprocess communication pathways supporting communicationthrough any communications protocol. The pathways can function insequence or in parallel, continuously or intermittently. The pathwayscan use any of the communications standards, protocols or technologies,described herein with respect to a communications network, in additionto standard parallel instruction sets used by many computers.

The nodes can include any entities capable of performing processingfunctions. Examples of such nodes that can be used with the embodimentsinclude computers (such as personal computers, workstations, servers, ormainframes), handheld wireless devices and wireline devices (such aspersonal digital assistants (PDAs), modem cell phones with processingcapability, wireless email devices including BlackBerry™ devices),document processing devices (such as scanners, printers, facsimilemachines, or multifunction document machines), or complex entities (suchas local-area networks or wide area networks) to which are connected acollection of processors, as described. For example, in the context ofthe present disclosure, a node itself can be a wide-area network (WAN),a local-area network (LAN), a private network (such as a Virtual PrivateNetwork (VPN)), or collection of networks.

Communications between the nodes can be made possible by acommunications network. A node can be connected either continuously orintermittently with communications network. As an example, in thecontext of the present disclosure, a communications network can be adigital communications infrastructure providing adequate bandwidth andinformation security.

The communications network can include wireline communicationscapability, wireless communications capability, or a combination ofboth, at any frequencies, using any type of standard, protocol ortechnology. In addition, in the present embodiments, the communicationsnetwork can be a private network (for example, a VPN) or a publicnetwork (for example, the Internet).

A non-inclusive list of example wireless protocols and technologies usedby a communications network can include Bluetooth™, general packet radioservice (GPRS), cellular digital packet data (CDPD), mobile solutionsplatform (MSP), multimedia messaging (MMS), wireless applicationprotocol (WAP), code division multiple access (CDMA), short messageservice (SMS), wireless markup language (WML), handheld device markuplanguage (HDML), binary runtime environment for wireless (BREW), radioaccess network (RAN), and packet switched core networks (PS-CN). Alsoincluded are various generation wireless technologies. An examplenon-inclusive list of primarily wireline protocols and technologies usedby a communications network includes asynchronous transfer mode (ATM),enhanced interior gateway routing protocol (EIGRP), frame relay (FR),high-level data link control (HDLC), Internet control message protocol(ICMP), interior gateway routing protocol (IGRP), internetwork packetexchange (IPX), ISDN, point-to-point protocol (PPP), transmissioncontrol protocol/internet protocol (TCP/IP), routing informationprotocol (RIP) and user datagram protocol (UDP). As skilled persons willrecognize, any other known or anticipated wireless or wireline protocolsand technologies can be used.

Embodiments of the present disclosure can include apparatuses forperforming the operations herein. An apparatus can be speciallyconstructed for the desired purposes, or it can comprise general purposecomputer system(s) selectively activated or reconfigured by a programstored in the computer system(s).

In one or more embodiments, the present embodiments are embodied inmachine-executable instructions. The instructions can be used to cause aprocessing device, for example a general-purpose or special-purposeprocessor, which is programmed with the instructions, to perform thesteps of the present disclosure. Alternatively, the steps of the presentdisclosure can be performed by specific hardware components that containhardwired logic for performing the steps, or by any combination ofprogrammed computer components and custom hardware components. Forexample, the present disclosure can be provided as a computer programproduct, as outlined above. In this environment, the embodiments caninclude a machine-readable medium having instructions stored on it. Theinstructions can be used to program any processor or processors (orother electronic devices) to perform a process or method according tothe present example embodiments. In addition, the present disclosure canalso be downloaded and stored on a computer program product. Here, theprogram can be transferred from a remote computer (e.g., a server) to arequesting computer (e.g., a client) by way of data signals embodied ina carrier wave or other propagation medium via a communication link(e.g., a modem or network connection) and ultimately such signals can bestored on the computer systems for subsequent execution.

The methods can be implemented in a computer program product accessiblefrom a computer-usable or computer-readable storage medium that providesprogram code for use by or in connection with a computer or anyinstruction execution system. A computer-usable or computer-readablestorage medium can be any apparatus that can contain or store theprogram for use by or in connection with the computer or instructionexecution system, apparatus, or device.

A data processing system suitable for storing and/or executing thecorresponding program code can include at least one processor coupleddirectly or indirectly to computerized data storage devices such asmemory elements. Input/output (I/O) devices (including but not limitedto keyboards, displays, pointing devices, etc.) can be coupled to thesystem. Network adapters can also be coupled to the system to enable thedata processing system to become coupled to other data processingsystems or remote printers or storage devices through interveningprivate or public networks. T₀ provide for interaction with a user, thefeatures can be implemented on a computer with a display device, such asan LCD (liquid crystal display), or another type of monitor fordisplaying information to the user, and a keyboard and an input device,such as a mouse or trackball by which the user can provide input to thecomputer.

A computer program can be a set of instructions that can be used,directly or indirectly, in a computer. The systems and methods describedherein can be implemented using programming languages such as CUDA,OpenCL, Flash™ JAVA™, C++, C, C#, Python, Visual Basic™, JavaScript™PHP, XML, HTML, etc., or a combination of programming languages,including compiled or interpreted languages, and can be deployed in anyform, including as a stand-alone program or as a module, component,subroutine, or other unit suitable for use in a computing environment.The software can include, but is not limited to, firmware, residentsoftware, microcode, etc. Protocols such as SOAP/HTTP can be used inimplementing interfaces between programming modules. The components andfunctionality described herein can be implemented on any desktopoperating system executing in a virtualized or non-virtualizedenvironment, using any programming language suitable for softwaredevelopment, including, but not limited to, different versions ofMicrosoft Windows™, Apple™ Mac™, iOS™, Unix™/X-Windows™, Linux™, etc.The system could be implemented using a web application framework, suchas Ruby on Rails.

Suitable processors for the execution of a program of instructionsinclude, but are not limited to, general and special purposemicroprocessors, and the sole processor or one of multiple processors orcores, of any kind of computer. A processor can receive and storeinstructions and data from a computerized data storage device such as aread-only memory, a random access memory, both, or any combination ofthe data storage devices described herein. A processor can include anyprocessing circuitry or control circuitry operative to control theoperations and performance of an electronic device.

The systems, modules, and methods described herein can be implementedusing any combination of software or hardware elements. The systems,modules, and methods described herein can be implemented using one ormore virtual machines operating alone or in combination with one other.Any applicable virtualization solution can be used for encapsulating aphysical computing machine platform into a virtual machine that isexecuted under the control of virtualization software running on ahardware computing platform or host. The virtual machine can have bothvirtual system hardware and guest operating system software.

The systems and methods described herein can be implemented in computersystem(s) that includes a back-end component, such as a data server, orthat includes a middleware component, such as an application server oran Internet server, or that includes a front-end component, such as aclient computer having a graphical user interface or an Internetbrowser, or any combination of them. The components of the computersystem(s) can be connected by any form or medium of digital datacommunication such as a communication network. Examples of communicationnetworks include, e.g., a LAN, a WAN, and the computers and networksthat form the Internet.

One or more embodiments of the present disclosure can be practiced withother computer system configurations, including hand-held devices,microprocessor systems, microprocessor-based or programmable consumerelectronics, minicomputers, mainframe computers, etc. The systems andmethods described herein can also be practiced in distributed computingenvironments where tasks are performed by remote processing devices thatare linked through a network.

The terms “computer program medium” and “computer readable medium” canbe used to generally refer to media such as but not limited to removablestorage drive, a hard disk installed in hard disk drive. These computerprogram products can provide software to computer system. The systemsand methods described herein can be directed to such computer programproducts.

References to “one embodiment,” “an embodiment,” “example embodiment,”“various embodiments,” etc., can indicate that the embodiment(s) of thepresent disclosure can include a particular feature, structure, orcharacteristic, but not every embodiment necessarily includes theparticular feature, structure, or characteristic. Further, repeated useof the phrase “in one embodiment,” or “in an example embodiment,” do notnecessarily refer to the same embodiment, although they can. Similarly,references to “instances” can indicate that various instance(s) of thepresent disclosure can include a particular feature, structure, orcharacteristic, but not every instance necessarily includes theparticular feature, structure, or characteristic. Further, repeated useof the phrase “in some instances” does not necessarily refer to the sameinstance, although it can.

In the description and claims, the terms “coupled” and “connected,”along with their derivatives, can be used. It should be understood thatthese terms can be not intended as synonyms for each other. Rather, inparticular embodiments, “connected” can be used to indicate that two ormore elements are in direct physical or electrical contact with eachother. “Coupled” can mean that two or more elements are in directphysical or electrical contact. However, “coupled” can also mean thattwo or more elements are not in direct contact with each other, but yetstill co-operate or interact with each other.

An algorithm can be here, and generally, considered to be aself-consistent sequence of acts or operations leading to a desiredresult. These include physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofelectrical or magnetic signals capable of being stored, transferred,combined, compared, and otherwise manipulated. It has proven convenientat times, principally for reasons of common usage, to refer to thesesignals as bits, values, elements, symbols, characters, terms, numbersor the like. It should be understood, however, that all of these andsimilar terms are to be associated with the appropriate physicalquantities and are merely convenient labels applied to these quantities.

Unless specifically stated otherwise, it can be appreciated thatthroughout the specification terms such as “processing,” “computing,”“calculating,” “determining,” or the like, refer to the action and/orprocesses of a computer or computer system, or similar electroniccomputer system(s), that manipulate and/or transform data represented asphysical, such as electronic, quantities within the computer system'sregisters and/or memories into other data similarly represented asphysical quantities within the computer system's memories, registers orother such information storage, transmission or display devices.

In a similar manner, the term “processor” can refer to any device orportion of a device that processes electronic data from registers and/ormemory to transform that electronic data into other electronic data thatcan be stored in registers and/or memory. As non-limiting examples,“processor” can be a Central Processing Unit (CPU) or a GraphicsProcessing Unit (GPU). A “computing platform” can comprise one or moreprocessors. As used herein, “software” processes can include, forexample, software and/or hardware entities that perform work over time,such as tasks, threads, and intelligent agents. Also, each process canrefer to multiple processes, for carrying out instructions in sequenceor in parallel, continuously or intermittently. The terms “system” and“method” are used herein interchangeably insofar as the system canembody one or more methods and the methods can be considered as asystem.

While one or more embodiments have been described, various alterations,additions, permutations and equivalents thereof are included within thescope of the disclosure.

In the description of embodiments, reference is made to the accompanyingdrawings that form a part hereof, which show by way of illustrationspecific embodiments of the claimed subject matter. It is to beunderstood that other embodiments can be used and that changes oralterations, such as structural changes, can be made. Such embodiments,changes or alterations are not necessarily departures from the scopewith respect to the intended claimed subject matter. While the stepsherein can be presented in a certain order, in some cases the orderingcan be changed so that certain inputs are provided at different times orin a different order without changing the function of the systems andmethods described. The disclosed procedures could also be executed indifferent orders. Additionally, various computations that are hereinneed not be performed in the order disclosed, and other embodimentsusing alternative orderings of the computations could be readilyimplemented. In addition to being reordered, the computations could alsobe decomposed into sub-computations with the same results.

Although the discussion above sets forth example implementations of thedescribed techniques, other architectures can be used to implement thedescribed functionality, and are intended to be within the scope of thisdisclosure. Furthermore, although specific distributions ofresponsibilities are defined above for purposes of discussion, thevarious functions and responsibilities might be distributed and dividedin different ways, depending on circumstances.

Furthermore, although the subject matter has been described in languagespecific to structural features and/or methodological acts, it is to beunderstood that the subject matter defined in the appended claims is notnecessarily limited to the specific features or acts described. Rather,the specific features and acts are disclosed as example forms ofimplementing the claims.

Example Clauses

A. A system for implementing a control algorithm for an autonomousvehicle, the system comprising: one or more processors; and one or morecomputer readable storage media communicatively coupled to the one ormore processors and storing instructions that are executable by the oneor more processors to: receive one or more symbols, the one or moresymbols including at least one static symbol or at least one dynamicsymbol; determine, based at least in part on the one or more symbols,one or more features; determine, based at least in part on the one ormore symbols or the one or more features, one or more predicates;determine, based at least in part on the one or more symbols, one ormore features, or one or more predicates, one or more linear temporallogic (LTL) formulas; determine, based at least in part on the one ormore LTL formulas, one or more automaton; utilize a Monte Carlo TreeSearch (MCTS) to generate one or more candidate trajectories; evaluatethe one or more candidate trajectories using the one or more automaton,wherein the one or more automaton verifies that the one or morecandidate trajectories satisfies the one or more LTL formulas associatedwith the one or more automaton; determine, based at least in part on acost function, a cost associated with a trajectory of the one or morecandidate trajectories; select, as a selected trajectory, the trajectoryof the one or more trajectories based at least in part on the cost; andcontrol the autonomous vehicle based at least in part on the selectedtrajectory.

B. A system as paragraph A recites, the instructions further executableby the one or more processors to receive the one or more symbols from atleast one of map data representing at least a portion of an environmentor from a perception system of the autonomous vehicle that determinesthe one or more symbols using sensor data captured by the autonomousvehicle.

C. A system as paragraph A or B recites, the instructions furtherexecutable by the one or more processors to evaluate the one or morefeatures based at least in part on the one or more symbols to return anumerical value associated with the one or more symbols.

D. A system as any one of paragraphs A-C recite, the instructionsfurther executable by the one or more processors to evaluate the one ormore predicates based at least in part on at least one of the one ormore symbols or the one or more features to return at least one of aBoolean value or a confidence level associated with a state of the oneor more symbols or the one or more features.

E. A system as any one of paragraphs A-D recite, the instructionsfurther executable by the one or more processors to add at least onenode to the MCTS based at least in part on a machine learning algorithmcomprising a neural network.

F. A system as any one of paragraphs A-E recite, wherein a first node ofthe MCTS includes a snapshot of an environment including the one or moresymbols, the one or more features, the one or more predicates, and theone or more LTL formulas, and wherein the instructions are furtherexecutable by the one or more processors to add a second node to theMCTS that includes an update of the environment associated with thesnapshot over time.

G. A system as any one of paragraphs A-F recite, the instructionsfurther executable by the one or more processors to: determine that theselected trajectory satisfies the one or more LTL formulas; anddetermine that the cost associated with the selected trajectory is alowest cost with respect to trajectories of the one or more candidatetrajectories that satisfy the one or more LTL formulas.

H. A system as any one of paragraphs A-G recite, the instructionsfurther executable by the one or more processors to: determine that acandidate trajectory of the one or more candidate trajectories violates,as a violation, the one or more LTL formulas associated with the one ormore automaton; and assign a penalty to the candidate trajectory basedat least in part on a degree of the violation of the one or more LTLformulas.

I. A method comprising: determining one or more symbols of anenvironment proximate to an autonomous vehicle; generating a context ofthe environment based at least in part on the one or more symbols;populating a tree search with one or more candidate trajectories;selecting, as a selected trajectory, a trajectory of the one or morecandidate trajectories based at least part on an evaluation of theselected trajectory with respect to one or more temporal logic formulasor on one or more costs; and commanding the autonomous vehicle based atleast in part on the selected trajectory.

J. A method as paragraph I recites, further comprising: populating thetree search with a first snapshot of the environment, the first snapshotbased at least in part on the environment at a first time; selecting anaction based at least in part on the first snapshot and at least onemachine learning algorithm; evolving the first snapshot over a time stepto generate a second snapshot, the evolving including applying theaction to the first snapshot; and adding a node to the tree search basedat least in part on the second snapshot, the node representing aspeculative snapshot associated with the environment associated with asecond time after the first time.

K. A method as paragraph I or J recites, wherein generating the contextincludes: determining one or more features based at least in part on theone or more symbols; determining one or more predicates based at leastin part on the one or more symbols or the one or more features; anddetermining the one or more temporal logic formulas based at least inpart on the one or more symbols, the one or more features, and the oneor more predicates.

L. A method as any one of paragraphs I-K recite, further comprisingselecting a fallback trajectory to implement in the event of a failureof one or more components of the autonomous vehicle.

M. A method as any one of paragraphs I-L recite, wherein the at leastone symbol includes a dynamic symbol representing a vehicle proximate tothe automatous vehicle, and wherein the one or more candidatetrajectories are based at least in part on a prediction associated witha motion of the dynamic symbol over time.

N. A method as any one of paragraphs I-M recite, further comprisinggenerating one or more automaton based at least in part on the one ormore temporal logic formulas, the method further comprising evaluatingthe one or more candidate trajectories using the one or more automaton,wherein the one or more automaton includes at least one of a Rabinautomaton, a Büchi automaton, a Streett automaton, a Parity automaton,or a Muller automaton.

O. A system comprising: one or more processors; and one or more computerreadable storage media communicatively coupled to the one or moreprocessors and storing instructions that are executable by the one ormore processors to: determine one or more symbols of an environmentproximate to an autonomous vehicle; generate a context of theenvironment based at least in part on the one or more symbols; populatea tree search with one or more candidate trajectories; select, as aselected trajectory, a trajectory of the one or more candidatetrajectories based at least part on an evaluation of the selectedtrajectory with respect to one or more temporal logic formulas or on oneor more costs; and command the autonomous vehicle based at least in parton the selected trajectory.

P. A system as paragraph O recites, the instructions further executableby the one or more processors to: populate the tree search with a firstsnapshot of the environment, the first snapshot based at least in parton the environment at a first time; select an action based at least inpart on the first snapshot and at least one machine learning algorithm;evolve the first snapshot over a time step by applying the action to thefirst snapshot to generate a second snapshot; and add a node to the treesearch based at least in part on a termination condition associated withthe action, the node representing a speculative snapshot associated withthe environment associated with a second time after the first time.

Q. A system as paragraph O or P recites, the instructions furtherexecutable by the one or more processors to: determine one or morefeatures based at least in part on the one or more symbols; determineone or more predicates based at least in part on the one or more symbolsor the one or more features; and determine the one or more temporallogic formulas based at least in part on the one or more symbols, theone or more features, and the one or more predicates.

R. A system as any one of paragraphs O-Q recite, wherein the temporallogic formulas include at least one of linear temporal logic (LTL)formulas or signal temporal logic (STL) formulas.

S. A system as any one of paragraphs O-R recite, wherein the at leastone symbol includes a dynamic symbol representing a vehicle proximate tothe automatous vehicle, and wherein the one or more candidatetrajectories are based at least in part on a prediction associated witha motion of the dynamic symbol over time.

T. A system as any one of paragraphs O-S recite, the instructionsfurther executable by the one or more processors to: generate one ormore automaton based at least in part on the one or more temporal logicformulas; and evaluate the one or more candidate trajectories using theone or more automaton, wherein the one or more automaton includes atleast one of a Rabin automaton, a Büchi automaton, a Streett automaton,a Parity automaton, or a Muller automaton.

While the example clauses described above are described with respect toone particular implementation, it should be understood that, in thecontext of this document, the content of the example clauses can also beimplemented via a method, device, system, and/or computer storage media.

What is claimed is:
 1. A system for implementing a control algorithm foran autonomous vehicle, the system comprising: one or more processors;and one or more computer readable storage media communicatively coupledto the one or more processors and storing instructions that areexecutable by the one or more processors to: receive one or moresymbols, the one or more symbols including at least one static symbol orat least one dynamic symbol; determine, based at least in part on theone or more symbols, one or more features; determine, based at least inpart on the one or more symbols or the one or more features, one or morepredicates; determine, based at least in part on the one or moresymbols, one or more features, or one or more predicates, one or morelinear temporal logic (LTL) formulas; determine, based at least in parton the one or more LTL formulas, one or more automaton; utilize a MonteCarlo Tree Search (MCTS) to generate one or more candidate trajectories;evaluate the one or more candidate trajectories using the one or moreautomaton, wherein the one or more automaton verifies that the one ormore candidate trajectories satisfies the one or more LTL formulasassociated with the one or more automaton; determine, based at least inpart on a cost function, a cost associated with a trajectory of the oneor more candidate trajectories; select, as a selected trajectory, thetrajectory of the one or more candidate trajectories based at least inpart on the cost; and control the autonomous vehicle based at least inpart on the selected trajectory.
 2. The system of claim 1, theinstructions further executable by the one or more processors to receivethe one or more symbols from at least one of map data representing atleast a portion of an environment or from a perception system of theautonomous vehicle that determines the one or more symbols using sensordata captured by the autonomous vehicle.
 3. The system of claim 1, theinstructions further executable by the one or more processors toevaluate the one or more features based at least in part on the one ormore symbols to return a numerical value associated with the one or moresymbols.
 4. The system of claim 1, the instructions further executableby the one or more processors to evaluate the one or more predicatesbased at least in part on at least one of the one or more symbols or theone or more features to return at least one of a Boolean value or aconfidence level associated with a state of the one or more symbols orthe one or more features.
 5. The system of claim 1, the instructionsfurther executable by the one or more processors to add at least onenode to the MCTS based at least in part on a machine learning algorithmcomprising a neural network.
 6. The system of claim 1, wherein a firstnode of the MCTS includes a snapshot of an environment including the oneor more symbols, the one or more features, the one or more predicates,and the one or more LTL formulas, and wherein the instructions arefurther executable by the one or more processors to add a second node tothe MCTS that includes an update of the environment associated with thesnapshot over time.
 7. The system of claim 1, the instructions furtherexecutable by the one or more processors to: determine that the selectedtrajectory satisfies the one or more LTL formulas; and determine thatthe cost associated with the selected trajectory is a lowest cost withrespect to trajectories of the one or more candidate trajectories thatsatisfy the one or more LTL formulas.
 8. The system of claim 1, theinstructions further executable by the one or more processors to:determine that a candidate trajectory of the one or more candidatetrajectories violates, as a violation, the one or more LTL formulasassociated with the one or more automaton; and assign a penalty to thecandidate trajectory based at least in part on a degree of the violationof the one or more LTL formulas.
 9. A method comprising: determining oneor more symbols of an environment proximate to an autonomous vehicle;generating a context of the environment based at least in part on theone or more symbols; populating a tree search with one or more candidatetrajectories; selecting, as a selected trajectory, a trajectory of theone or more candidate trajectories based at least part on an evaluationof the selected trajectory with respect to one or more temporal logicformulas or on one or more costs; and controlling the autonomous vehiclebased at least in part on the selected trajectory.
 10. The method ofclaim 9, further comprising: populating the tree search with a firstsnapshot of the environment, the first snapshot based at least in parton the environment at a first time; selecting an action based at leastin part on the first snapshot and at least one machine learningalgorithm; evolving the first snapshot over a time step to generate asecond snapshot, the evolving including applying the action to the firstsnapshot; and adding a node to the tree search based at least in part onthe second snapshot, the node representing a speculative snapshotassociated with the environment associated with a second time after thefirst time.
 11. The method of claim 9, wherein generating the contextincludes: determining one or more features based at least in part on theone or more symbols; determining one or more predicates based at leastin part on the one or more symbols or the one or more features; anddetermining the one or more temporal logic formulas based at least inpart on the one or more symbols, the one or more features, and the oneor more predicates.
 12. The method of claim 9, further comprisingselecting a fallback trajectory to implement in an event of a failure ofone or more components of the autonomous vehicle.
 13. The method ofclaim 9, wherein the one or more symbols comprise a dynamic symbolrepresenting a vehicle proximate to the autonomous vehicle, and whereinthe one or more candidate trajectories are based at least in part on aprediction associated with a motion of the dynamic symbol over time. 14.The method of claim 9, further comprising generating one or moreautomaton based at least in part on the one or more temporal logicformulas, the method further comprising evaluating the one or morecandidate trajectories using the one or more automaton, wherein the oneor more automaton includes at least one of a Rabin automaton, a Büchiautomaton, a Streett automaton, a Parity automaton, or a Mullerautomaton.
 15. A system comprising: one or more processors; and one ormore computer readable storage media communicatively coupled to the oneor more processors and storing instructions that are executable by theone or more processors to: determine one or more symbols of anenvironment proximate to an autonomous vehicle; generate a context ofthe environment based at least in part on the one or more symbols;populate a tree search with one or more candidate trajectories; select,as a selected trajectory, a trajectory of the one or more candidatetrajectories based at least part on an evaluation of the selectedtrajectory with respect to one or more temporal logic formulas or on oneor more costs; and control the autonomous vehicle based at least in parton the selected trajectory.
 16. The system of claim 15, the instructionsfurther executable by the one or more processors to: populate the treesearch with a first snapshot of the environment, the first snapshotbased at least in part on the environment at a first time; select anaction based at least in part on the first snapshot and at least onemachine learning algorithm; evolve the first snapshot over a time stepby applying the action to the first snapshot to generate a secondsnapshot; and add a node to the tree search based at least in part on atermination condition associated with the action, the node representinga speculative snapshot associated with the environment associated with asecond time after the first time.
 17. The system of claim 15, theinstructions further executable by the one or more processors to:determine one or more features based at least in part on the one or moresymbols; determine one or more predicates based at least in part on theone or more symbols or the one or more features; and determine the oneor more temporal logic formulas based at least in part on the one ormore symbols, the one or more features, and the one or more predicates.18. The system of claim 15, wherein the temporal logic formulas includeat least one of linear temporal logic (LTL) formulas or signal temporallogic (STL) formulas.
 19. The system of claim 15, wherein the one ormore symbols comprise a dynamic symbol representing a vehicle proximateto the autonomous vehicle, and wherein the one or more candidatetrajectories are based at least in part on a prediction associated witha motion of the dynamic symbol over time.
 20. The system of claim 15,the instructions further executable by the one or more processors to:generate one or more automaton based at least in part on the one or moretemporal logic formulas; and evaluate the one or more candidatetrajectories using the one or more automaton, wherein the one or moreautomaton includes at least one of a Rabin automaton, a Büchi automaton,a Streett automaton, a Parity automaton, or a Muller automaton.